### Introduction Of Signals And Systems notes, questions and answers

# Introduction Of Signals And Systems

## Digital Signal Processing

## Digital

In digital communication, we use discrete signals to represent data using binary numbers.

## Signal

A signal is anything that carries some information. It’s a physical quantity that conveys data and varies with time, space, or any other independent variable. It can be in the time/frequency domain. It can be one-dimensional or two-dimensional.

## Processing

The performing of operations on any data in accordance with some protocol or instruction is known as processing.

## System

A system is a physical entity that is responsible for the processing. It has the necessary hardware to perform the required arithmetic or logical operations on a signal.

# Digital Signal Processing

## What is Digital Signal Processing?

### Digital

### Signal

### Processing

The performing of operations on any data in accordance with some protocol or instruction is known as processing.

## A DSP contains these key components

- Program Memory: Stores the programs the DSP will use to process data
- Data Memory: Stores the information to be processed
- Compute Engine: Performs the math processing, accessing the program from the Program Memory and the data from the Data Memory
- Input/Output: Serves a range of functions to connect to the outside world

- Program Memory: Stores the programs the DSP will use to process data
- Data Memory: Stores the information to be processed
- Compute Engine: Performs the math processing, accessing the program from the Program Memory and the data from the Data Memory
- Input/Output: Serves a range of functions to connect to the outside world

## elements of Digital Signal Processing

## Anti-Aliasing-Filter

The I/o signal is applying to the antialiasing filter.this is a lowpass filter used to remove the high-frequency noise and Band limit the Signal

The I/o signal is applying to the antialiasing filter.this is a lowpass filter used to remove the high-frequency noise and Band limit the Signal

## Sample&Hold

this device provides the input to the ADC and will be required if the i/o signal was not proper and flute.

this device provides the input to the ADC and will be required if the i/o signal was not proper and flute.

## A/D conveter

this a conveter which converts the Analog S/g to the digital.

this a conveter which converts the Analog S/g to the digital.

## DSP

this gives the better quality signal

this gives the better quality signal

## D/A Conveter

this device reconvenes the signal from digital S/g to the Analog.

this device reconvenes the signal from digital S/g to the Analog.

## Reconstruction filter

this filter is used to construct the signal properly after the signal processing.

this filter is used to construct the signal properly after the signal processing.

## Block diagram of a DSP system

## The first step is to get an electrical signal. The transducer (in our case, a microphone) converts sound into an electrical signal. You can use any transducer depending upon the case. Once you have an analog electrical signal, we pass it through an operational amplifier (Op-Amp) to condition the analog signal. Basically, we amplify the signal. Or limit it to protect the next stages. The anti-aliasing filter is an essential step in the conversion of analog to a digital signal. It is a low-pass filter. Meaning, it allows frequencies up to a certain threshold to pass. It attenuates all frequencies above this threshold. These unwanted frequencies make it difficult to sample an analog signal.

The next stage is a simple analog-to-digital converter (ADC). This unit takes in analog signals and outputs a stream of binary digits. The heart of the system is the digital signal processor. These days we use CMOS chips (even ULSI) to make digital signal processors. In fact, modern processors, like the Cortex M4 have DSP units built inside the SoC. These processor units have high-speed, high data throughputs, and dedicated instruction sets. The next stages are sort of the opposite of the stages preceding the digital signal processor.

The digital-to-analog converter does what its name implies. It’s necessary for the slew rate of the DAC to match the acquisition rate of the ADC. The smoothing filter is another low-pass filter that smoothes the output by removing unwanted high-frequency components. The last op-amp is just an amplifier. The output transducer is a speaker in our case. You can use anything else according to your requirements.

The next stage is a simple analog-to-digital converter (ADC). This unit takes in analog signals and outputs a stream of binary digits. The heart of the system is the digital signal processor. These days we use CMOS chips (even ULSI) to make digital signal processors. In fact, modern processors, like the Cortex M4 have DSP units built inside the SoC. These processor units have high-speed, high data throughputs, and dedicated instruction sets. The next stages are sort of the opposite of the stages preceding the digital signal processor.

The digital-to-analog converter does what its name implies. It’s necessary for the slew rate of the DAC to match the acquisition rate of the ADC. The smoothing filter is another low-pass filter that smoothes the output by removing unwanted high-frequency components. The last op-amp is just an amplifier. The output transducer is a speaker in our case. You can use anything else according to your requirements.

## Advantages of a Digital Signal Processing

- DSP has a high level of accuracy. The filters designed in DSP have firm control over output accuracy as compared to analog filters.
- The reconfiguration in an analog system is very much tough because the entire hardware and its component will have to be changed. On the contrary, a DSP reconfiguration is much more comfortable as only the code, or the DSP program needs to be flashed after making the changes according to the requirements.
- The combination of DSP interfaced with FPGA helps in designing the protocol stack of the whole wireless system like WiMAX, LTE, etc.
- Implementation in digital is much more cost effective than its analog counterpart.
- The digital system in DSP can be easily cascaded without any problems in loading.
- Digital circuits can be easily reproduced in huge quantities cost effectively.
- Accessible transportation is possible because digital signals can be processed offline.
- Using the DSP method sophisticated signal processing algorithms can be implemented.

- DSP has a high level of accuracy. The filters designed in DSP have firm control over output accuracy as compared to analog filters.
- The reconfiguration in an analog system is very much tough because the entire hardware and its component will have to be changed. On the contrary, a DSP reconfiguration is much more comfortable as only the code, or the DSP program needs to be flashed after making the changes according to the requirements.
- The combination of DSP interfaced with FPGA helps in designing the protocol stack of the whole wireless system like WiMAX, LTE, etc.
- Implementation in digital is much more cost effective than its analog counterpart.
- The digital system in DSP can be easily cascaded without any problems in loading.
- Digital circuits can be easily reproduced in huge quantities cost effectively.
- Accessible transportation is possible because digital signals can be processed offline.
- Using the DSP method sophisticated signal processing algorithms can be implemented.

## Disadvantages of a Digital Signal Processing

- When using DSP, there is a need for using anti-aliasing filter before ADC ( Analog To Digital Converter) as well as using a reconstruction filter after DAC (Digital to Analog Converter). Due to the use of this extra two modules viz. ADC and DAC, the complexity of DSP based hardware increases.
- Digital Signal Processing(DSP) processes the signal at high speed and comprises of more top internal hardware resources.
- Each DSP has a different hardware architecture and software instructions.
- One needs to cautiously use the IC as per hardware and software requirements as most of the DSP chip is very expensive.
- Only in a synchronized communication system, the detection of digital signals is possible but it not so in the case of analog systems.
- Higher bandwidth is required for digital communication than analog for transmission of the same information.

- When using DSP, there is a need for using anti-aliasing filter before ADC ( Analog To Digital Converter) as well as using a reconstruction filter after DAC (Digital to Analog Converter). Due to the use of this extra two modules viz. ADC and DAC, the complexity of DSP based hardware increases.
- Digital Signal Processing(DSP) processes the signal at high speed and comprises of more top internal hardware resources.
- Each DSP has a different hardware architecture and software instructions.
- One needs to cautiously use the IC as per hardware and software requirements as most of the DSP chip is very expensive.
- Only in a synchronized communication system, the detection of digital signals is possible but it not so in the case of analog systems.
- Higher bandwidth is required for digital communication than analog for transmission of the same information.

## Applications

**General application areas for DSP include****Audio signal processing****Audio data compression e.g. MP3****Video data compression****Computer graphics****Digital image processing****Photo manipulation****Speech processing****Speech recognition****Data transmission****Radar****Sonar****Financial signal processing****Economic forecasting****Seismology****Biomedicine****Weather forecasting**

**General application areas for DSP include****Audio signal processing****Audio data compression e.g. MP3****Video data compression****Computer graphics****Digital image processing****Photo manipulation****Speech processing****Speech recognition****Data transmission****Radar****Sonar****Financial signal processing****Economic forecasting****Seismology****Biomedicine****Weather forecasting**

## Analog To Digital Conversion

## An analog-to-digital converter (abbreviated ADC, A/D or A to D) is a device that converts a continuous quantity to a discrete digital number. Or A device that converts continuously varying analog signals from instruments and sensors that monitor conditions, such as sound, movement and temperature into binary code for the computer. The A/D converter may be contained on a single chip or can be one circuit within a chip.Analog to Digital Converter (ADC) is an electronic integrated circuit used to convert the analog signals such as voltages to digital or binary form consisting of 1s and 0s. Most of the ADCs take a voltage input as 0 to 10V, -5V to +5V, etc., and correspondingly produces digital output as some sort of a binary number.**Analog**: continuously valued signal, such as temperature or speed, with infinite possible values in between **Digital**: discretely valued signal, such as integers, encoded in binary Analog-to-digital converter: ADC, A/D, A2D; converts an analog signal to a digital signal

**Analog**: continuously valued signal, such as temperature or speed, with infinite possible values in between

**Digital**: discretely valued signal, such as integers, encoded in binary

## Analog signals

## directly measurable quantities in terms of some other quantity **Examples**Thermometer – mercury height rises as temperature risesCar Speedometer – Needle moves farther right as you accelerate

**Examples**

## Digital Signals

## have only two states. For digital computers, we refer to binary states, 0 and 1. “1” can be on, “0” can be off. **Examples**Light switch can be either on or offDoor to a room is either open or closed

**Examples**

## What is Analog to Digital Converter?

## A converter that is used to change the analog signal to digital is known as an analog to digital converter or ADC converter. This converter is one kind of integrated circuit or IC that converts the signal directly from continuous form to discrete form. This converter can be expressed in A/D, ADC, A to D. The inverse function of DAC is nothing but ADC. The analog to digital converter symbol is shown below.The process of converting an analog signal to digital can be done in several ways. There are different types of ADC chips available in the market from different manufacturers like the ADC08xx series. So, a simple ADC can be designed with the help of discrete components.The main features of ADC are sample rate and bit resolution.The sample rate of an ADC is nothing but how fast an ADC can convert the signal from analog to digital.Bit resolution is nothing but how much accuracy can an analog to digital converter can convert the signal from analog to digital.One of the major benefits of ADC converter is the high data acquisition rate even at multiplexed inputs. With the invention of a wide variety of ADC integrated circuits (IC’s), data acquisition from various sensors becomes more accurate and faster. Dynamic characteristics of the high-performance ADCs are improved measurement repeatability, low power consumption, precise throughput, high linearity, excellent Signal-to-Noise Ratio (SNR), and so on.A variety of applications of the ADCs areMeasurement and control systems, Industrial instrumentation, Communication systems, And all other sensory-based systems. Classification of ADCs based on factors like performance, bit rates, power, cost, etc.

## ADC Block Diagram

## The block diagram of ADC is shown above which includes sample, hold, quantize, and encoder. The process of ADC can be done like the following.First, the analog signal is applied to the first block namely a sample wherever it can be sampled at an exact sampling frequency. The amplitude value of the sample like an analog value can be maintained as well as held within the second block like Hold. The hold sample can be quantized into discrete value through the third block like quantize. Finally, the last block like encoder changes the discrete amplitude into a binary number.In ADC, the conversion of the signal from analog to digital can be explained through the above block diagram.

## Sample

## In the sample block, the analog signal can be sampled at an exact interval of time. The samples are used in continuous amplitude and hold real value however they are discrete with respect to time. While converting the signal, the sampling frequency plays an essential role. So it can be maintained at a precise rate. Based on the system requirement, the sampling rate can be fixed.

## Hold

## In ADC, HOLD is the second block and it doesn’t have any function because it simply holds the sample amplitude till the next sample is taken. So the value of hold doesn’t change until the next sample.

## Quantize

## In ADC, this is the third block which is mainly used for quantization. The main function of this is to convert the amplitude from continuous (analog) into discrete. The value of continuous amplitude within hold block moves throughout quantize block to turn into discrete in amplitude. Now, the signal will be in digital form because it includes discrete amplitude as well as time.

## Encoder

## The final block in ADC is an encoder that converts the signal from digital form to binary. We know that a digital device works by using binary signals. So it is required to change the signal from digital to binary with the help of an encoder. So this is the entire method to change an analog signal to digital using an ADC. The time taken for the entire conversion can be done within a microsecond.

## Analog to Digital Conversion Process

## There are many methods to convert analog signals to digital signals. These converters find more applications as an intermediate device to convert the signals from analog to digital form, display output on LCD through a microcontroller. The objective of an A/D converter is to determine the output signal word corresponding to an analog signal. Now we are going to see an ADC of 0804. It is an 8-bit converter with a 5V power supply. It can take only one analog signal as input.The digital output varies from 0-255. ADC needs a clock to operate. The time taken to convert the analog to digital value depends on the clock source. An external clock can be given to CLK IN pin no.4. A suitable RC circuit is connected between the clock IN and clock R pins to use the internal clock. Pin2 is the input pin – High to low pulse brings the data from the internal register to the output pins after conversion. Pin3 is a Write – Low to high pulse is given to the external clock. Pin11 to 18 are data pins from MSB to LSB.Analog to Digital Converter samples the analog signal on each falling or rising edge of the sample clock. In each cycle, the ADC gets the analog signal, measures it, and converts it into a digital value. The ADC converts the output data into a series of digital values by approximates the signal with fixed precision.In ADCs, two factors determine the accuracy of the digital value that captures the original analog signal. These are quantization level or bit rate and sampling rate. The below figure depicts how analog to digital conversion takes place. Bit rate decides the resolution of digitized output and you can observe in the below figure where 3-bit ADC is used for converting the analog signal.Assume that one-volt signal has to be converted from digital by using 3-bit ADC as shown below. Therefore, a total of 2^3=8 divisions are available for producing 1V output. This results 1/8=0.125V is called as minimum change or quantization level represented for each division as 000 for 0V, 001 for 0.125, and likewise upto 111 for 1V. If we increase the bit rates like 6, 8, 12, 14, 16, etc. we will get a better precision of the signal. Thus, bit rate or quantization gives the smallest output change in the analog signal value that results from a change in the digital representation.Suppose if the signal is about 0-5V and we have used 8-bit ADC then the binary output of 5V is 256. And for 3V it is 133There is an absolute chance of misrepresenting the input signal on the output side if it is sampled at a different frequency than the desired one. Therefore, another important consideration of the ADC is the sampling rate. The Nyquist theorem states that the acquired signal reconstruction introduces distortion unless it is sampled at (minimum) twice the rate of the largest frequency content of the signal as you can observe in the diagram. But this rate is 5-10 times the maximum frequency of the signal in practice.

## Factors

## The ADC performance can be evaluated through its performance based on different factors. From that, the following two main factors are- SNR (Signal-to-Noise Ratio)
- Bandwidth

- SNR (Signal-to-Noise Ratio)
- Bandwidth

## SNR (Signal-to-Noise Ratio)

## The SNR reflects the average number of bits without noise in any particular sample.

## Bandwidth

## The bandwidth of an ADC can be determined by estimating the sampling rate. The analog source can be sampled per second to produce discrete values.

## Types of Analog to Digital Converters

- Dual Slope A/D Converter
- Flash A/D Converter
- Successive Approximation A/D Converter
- Semi-flash ADC
- Sigma-Delta ADC
- Pipelined ADC

- Dual Slope A/D Converter
- Flash A/D Converter
- Successive Approximation A/D Converter
- Semi-flash ADC
- Sigma-Delta ADC
- Pipelined ADC

## Dual Slope A/D Converter

## In this type of ADC converter, comparison voltage is generated by using an integrator circuit which is formed by a resistor, capacitor, and operational amplifier combination. By the set value of Vref, this integrator generates a sawtooth waveform on its output from zero to the value Vref. When the integrator waveform is started correspondingly counter starts counting from 0 to 2^n-1 where n is the number of bits of ADC.When the input voltage Vin equal to the voltage of the waveform, then the control circuit captures the counter value which is the digital value of the corresponding analog input value. This Dual slope ADC is a relatively medium cost and slow speed device.

## Flash A/D Converter

## This ADC converter IC is also called parallel ADC, which is the most widely used efficient ADC in terms of its speed. This flash analog to digital converter circuit consists of a series of comparators where each one compares the input signal with a unique reference voltage. At each comparator, the output will be a high state when the analog input voltage exceeds the reference voltage. This output is further given to the priority encoder for generating binary code based on higher-order input activity by ignoring other active inputs. This flash type is a high-cost and high-speed device.

## Successive Approximation A/D Converter

## The SAR ADC a most modern ADC IC and much faster than dual slope and flash ADCs since it uses a digital logic that converges the analog input voltage to the closest value. This circuit consists of a comparator, output latches, successive approximation register (SAR), and D/A converter. At the start, SAR is reset and as the LOW to HIGH transition is introduced, the MSB of the SAR is set. Then this output is given to the D/A converter that produces an analog equivalent of the MSB, further it is compared with the analog input Vin. If comparator output is LOW, then MSB will be cleared by the SAR, otherwise, the MSB will be set to the next position. This process continues till all the bits are tried and after Q0, the SAR makes the parallel output lines to contain valid data.

## Semi-flash ADC

## These types of analog to digital converts mainly works approximately their limitation size through two separate flash converters, where each converter resolution is half of the bits for the semi-flush device. The capacity of a single flash converter is, it handles the MSBs (most significant bits) whereas the other handles the LSB (least significant bits).

## Sigma-Delta ADC

## Sigma Delta ADC (Î£Î”) is fairly a recent design. These are extremely slow as compared to other kinds of designs however they offer the maximum resolution for all kinds of ADC. Thus, they are extremely compatible with high-fidelity based audio applications, however, they are normally not utilizable wherever high BW (bandwidth) is required.

## Pipelined ADC

## Pipelined ADCs are also known as sub ranging quantizers which are related in concept to successive approximations, even though more sophisticated. While successive approximations grow through every step by going to the next MSB, this ADC uses the following process.- It is used for a coarse conversion. After that, it evaluates that change toward the input signal.
- This converter acts as a better conversion by allowing for a temporary conversion with a range of bits.
- Usually, pipelined designs offer a center ground among SARs as well as flash analog to digital converters by balancing its size, speed & high resolution.

- It is used for a coarse conversion. After that, it evaluates that change toward the input signal.
- This converter acts as a better conversion by allowing for a temporary conversion with a range of bits.
- Usually, pipelined designs offer a center ground among SARs as well as flash analog to digital converters by balancing its size, speed & high resolution.

## Advantages of ADC

- Flash ADCs are the fastest compared to the other Analog to Digital Converter.
- Compared to other converters, Sigma Delta ADCs offer high resolution at low-cost.
- Successive Approximation ADCs operate at high speed and are more reliable.
- Sigma-Delta ADCs have higher noise shaping capability and also offer high resolution.
- Pipelined ADCs also offer high resolution at high speed.

- Flash ADCs are the fastest compared to the other Analog to Digital Converter.
- Compared to other converters, Sigma Delta ADCs offer high resolution at low-cost.
- Successive Approximation ADCs operate at high speed and are more reliable.
- Sigma-Delta ADCs have higher noise shaping capability and also offer high resolution.
- Pipelined ADCs also offer high resolution at high speed.

## Disadvantages of ADC

- Circuit Complexity increases with the increase in the use of Comparators in Flash ADCs.
- Flash ADCs are expensive.
- Converting non-periodic signals using Pipeline ADCs can be difficult as it typically runs at a periodic rate.
- Pipeline ADCs are sensitive to board layout.
- Pipeline latency of the input signal occurs in Pipeline ADCs which causes non-linearities in the parameters like Offset and Gain.
- Successive Approximation converters used for higher resolution will be slower.

- Circuit Complexity increases with the increase in the use of Comparators in Flash ADCs.
- Flash ADCs are expensive.
- Converting non-periodic signals using Pipeline ADCs can be difficult as it typically runs at a periodic rate.
- Pipeline ADCs are sensitive to board layout.
- Pipeline latency of the input signal occurs in Pipeline ADCs which causes non-linearities in the parameters like Offset and Gain.
- Successive Approximation converters used for higher resolution will be slower.

## Applications of Analog to Digital Converter

- At present, the usage of digital devices is increasing. These devices work based on the digital signal. An analog to digital converter plays a key role in such kind of devices to convert the signal from analog to digital. The applications of analog to digital converters are limitless which are discussed below.
- AC (air conditioner) includes temperature sensors to maintain the temperature within the room. So this conversion of temperature can be done from analog to digital with the help of ADC.
- It is also used in a digital oscilloscope to convert the signal from analog to digital to display.
- ADC is used to convert the analog voice signal to digital in mobile phones because mobile phones use digital voice signals but actually, the voice signal is in the form of analog. So ADC is used to convert the signal before sending the signal toward the transmitter of the cell phone.
- ADC is used in medical devices like MRI and X-Ray to convert the images from analog to digital before alteration.
- The camera in the mobile mainly used for capturing images as well as videos. These are stored in the digital device, so these are converted to digital form using ADC.
- The cassette music can also be changed into a digital like CDS & thumb drives use ADC.
- At present ADC is used in every device because almost all devices available in the market are in digital version. So these devices use ADC.

- At present, the usage of digital devices is increasing. These devices work based on the digital signal. An analog to digital converter plays a key role in such kind of devices to convert the signal from analog to digital. The applications of analog to digital converters are limitless which are discussed below.
- AC (air conditioner) includes temperature sensors to maintain the temperature within the room. So this conversion of temperature can be done from analog to digital with the help of ADC.
- It is also used in a digital oscilloscope to convert the signal from analog to digital to display.
- ADC is used to convert the analog voice signal to digital in mobile phones because mobile phones use digital voice signals but actually, the voice signal is in the form of analog. So ADC is used to convert the signal before sending the signal toward the transmitter of the cell phone.
- ADC is used in medical devices like MRI and X-Ray to convert the images from analog to digital before alteration.
- The camera in the mobile mainly used for capturing images as well as videos. These are stored in the digital device, so these are converted to digital form using ADC.
- The cassette music can also be changed into a digital like CDS & thumb drives use ADC.
- At present ADC is used in every device because almost all devices available in the market are in digital version. So these devices use ADC.

## Types Of Signals

- Continuous-Time Signals
- Discrete-Time Signals
- Deterministic signals
- Non-Deterministic signals
- Even Signals
- Odd Signals
- Periodic Signals
- Non-Periodic Signals
- Energy Signals
- Power Signals
- Real Signals
- Imaginary Signals

- Continuous-Time Signals
- Discrete-Time Signals
- Deterministic signals
- Non-Deterministic signals
- Even Signals
- Odd Signals
- Periodic Signals
- Non-Periodic Signals
- Energy Signals
- Power Signals
- Real Signals
- Imaginary Signals

## Continuous-Time Signals

A Continuous-Time Signal is defined for all values of time. X is the dependent variable and t is the independent variable. When there is an X(t) for every single value of t, it is continuous.

A Continuous-Time Signal is defined for all values of time. X is the dependent variable and t is the independent variable. When there is an X(t) for every single value of t, it is continuous.

## Discrete-Time Signals

Discrete-Time Signals are defined only at certain discrete values referred to as n and denoted in square brackets.

Discrete-Time Signals are defined only at certain discrete values referred to as n and denoted in square brackets.

## Deterministic signals

A signal is said to be Deterministic when there is no doubt with respect to value at any instant of time. It can be easily identified and represented as a function, X(t).

A signal is said to be Deterministic when there is no doubt with respect to value at any instant of time. It can be easily identified and represented as a function, X(t).

## Non-Deterministic signals

A signal is said to be Non-Deterministic when it is basically the opposite of that of a Deterministic signal, which means there is uncertainty with respect to value at any instant of time.

A signal is said to be Non-Deterministic when it is basically the opposite of that of a Deterministic signal, which means there is uncertainty with respect to value at any instant of time.

## Even Signals

Even signals remain identical when they are reflected or mirrored across the y-axis.

Even signals remain identical when they are reflected or mirrored across the y-axis.

## Odd Signals

Odd signals are anti-symmetrical when they are reflected or mirrored across the y-axis.

Odd signals are anti-symmetrical when they are reflected or mirrored across the y-axis.

## Periodic Signals

A signal is said to be periodic when it repeats itself for a regular interval of time.

A signal is said to be periodic when it repeats itself for a regular interval of time.

## Non-Periodic Signals

A signal is said to be non-periodic when it has no pattern, when it does not repeat itself for a regular interval, no matter how large the time interval.

A signal is said to be non-periodic when it has no pattern, when it does not repeat itself for a regular interval, no matter how large the time interval.

## Energy Signals

Energy of power signal is infinity

Energy of power signal is infinity

## Power Signals

Power of energy signal is 0

Power of energy signal is 0

## Real Signals

A signal is said to be real when it satisfies condition x(t)=x*(t)

A signal is said to be real when it satisfies condition x(t)=x*(t)

## Imaginary Signals

A signal is said to be imaginary when it satisfies condition x(t)=-x*(t)

A signal is said to be imaginary when it satisfies condition x(t)=-x*(t)

## Systems

## Systems process input signals to produce output signals A system is combination of elements that manipulates one or more signals to accomplish a function and produces some output.

## Classification Of Systems

## The systems are classified as

- Static & dynamic system
- Time invariant and variant system
- Linear and non linear system
- Causal and non causal system
- Stable and unstable system

- Static & dynamic system
- Time invariant and variant system
- Linear and non linear system
- Causal and non causal system
- Stable and unstable system

## Static and dynamic system

## Static system is said to be a memoryless system. The output does not depend the past or future input. It only depends the present input for an output.

Ex:- y(n) = x(n)

Dynamic system is said to be as system with memory. Its output depend the past values of input for an output.

Ex:- Y(n) = x(n) + x(n - 1)

This static and dynamic systems are otherwise called as memoryless and system with memory.

Systems with and without memory

A system is called memory less if the output at any time t (or n) depends only on the input at time t (or n); in other words, independent of the input at times before of after t (or n).

Examples of memory less systems:- y(t) = rx(t)

Examples of systems with memory:- y[n]=x[n-1]

Ex:- y(n) = x(n)

Dynamic system is said to be as system with memory. Its output depend the past values of input for an output.

Ex:- Y(n) = x(n) + x(n - 1)

This static and dynamic systems are otherwise called as memoryless and system with memory.

Systems with and without memory

A system is called memory less if the output at any time t (or n) depends only on the input at time t (or n); in other words, independent of the input at times before of after t (or n).

Examples of memory less systems:- y(t) = rx(t)

Examples of systems with memory:- y[n]=x[n-1]

## Time invariant and time variant system

## If the time shifts in the input signals results in corresponding time shift in the output, then the system is called as time invariant. The input and output characteristics do not change with time.

f[x(t1 – t2)] = y(t1 – t2)

For a continuous time system,

f[x(t1 – t2)] = y(t1 – t2)

For a discrete time system,

F[x(n - k)] = y(n - k)

If the above relation does not satisfy, then the system is said to be a time variant system. A system is called time-invariant if the way it responds to inputs does not change over time

x(t)→y(t) ⇒ x(t-t0)→y(t-t0) for any t0

x(n)→y(n) ⇒ x(n-n0)→y(n-n0) for any n0

Examples of time-invariant systems

The RC circuit considered earlier provided the values of R or C are constant.

y[n] = x[n-1]

Examples of time-varying systems

The RC circuit considered earlier if the values of R or C change over time.

y(t) = x(2t) sinec

x(t) = x(2t) but x(t-t0)→ x(2t-t0)

Most physical systems are slowly time-varying due to aging, etc. Hence, they can be considered time-invariant for certain time periods in which its behavior does not change significantly.

**Linear and non linear system**

A system is said to be linear if it satisfies the superposition principle. Superposition principle states that the response to a weighted sum of input signal be equal to the weighted sum of the output corresponding to each of the individual input signal The continuous system is linear if,

F[a1x1(t) + a2x2(t)] = a1y1(t) + a2y2(t)

The discrete system is linear if,

F[a1x1(n) + a2x2(n)] = a1y1(n) + a2y2(n)

Otherwise the system is non linear. A system is called linear if its I/O behavior satisfies the additivity and homogeneity properties:

x1(t)→y1(t) ( x1(t)+x2(t))→(y1(t)+y2(t))

} ⇒

x2(t)→y2(t) (ax1(t)) →(ay1(t))

for any complex constant a.

Equivalently, a system is called linear if its I/O behavior satisfies the superposition property:

x1(t)→y1(t)

}⇒(ax1(t)+bx2(t))→(ay1(t)+by2(t))

x2(t)→y2(t)

where any complex constants a and b.

**Causal and non causal system**

A causal system is one whose output depends upon the present and past input values. If the system depends the future input values, the system is said to be non causal. Eg.for causal system.

Y(t) = x(t) + x(t - 1)

Y(n) = x(n) + x(n - 3)

Ex:- For non causal system,

Y(t) = x(t+3) + x2(t)

Y(n) = x(2n)

A system is called causal or non-anticipative if the output at any time t (or n) depends only on the input at times t or before t (or n or before n); in other words, independent of the input at times after t (or n). All memory less systems are causal. Physical systems where the time is the independent variable are causal. Non-causal systems may arise in applications where the independent variable is not the time such as in the image processing applications.

Examples of causal systems:

y[n] = x[n-1]

Examples of non-causal systems:

x(t) = x(-t)

**Stable and unstable system**

When every bounded input produces bounded output then the system is called as stable system or bounded input bounded output (BIBO stable). Otherwise the system is unstable. A system is called stable if it produces bounded outputs for all bounded inputs Stability in a physical system generally results from the presence of mechanisms that dissipate energy, such as the resistors in a circuit, friction in a mechanical system, etcNote: For a bounded signal, amplitude is finite.Example:- y (t) = x2(t)Let the input is u(t) (unit step bounded input) then the output y(t) = u2(t) = u(t) = bounded output. Hence, the system is stable.Example : - y (t) = ∫x(t)dt∫x(t)dtLet the input is u (t) (unit step bounded input) then the output y(t) = ∫u(t)dt∫u(t)dt = ramp signal (unbounded because amplitude of ramp is not finite it goes to infinite when t → infinite). Hence, the system is unstable.## Questions and answers

f[x(t1 – t2)] = y(t1 – t2)

For a continuous time system,

f[x(t1 – t2)] = y(t1 – t2)

For a discrete time system,

F[x(n - k)] = y(n - k)

If the above relation does not satisfy, then the system is said to be a time variant system. A system is called time-invariant if the way it responds to inputs does not change over time

x(t)→y(t) ⇒ x(t-t0)→y(t-t0) for any t0

x(n)→y(n) ⇒ x(n-n0)→y(n-n0) for any n0

Examples of time-invariant systems

The RC circuit considered earlier provided the values of R or C are constant.

y[n] = x[n-1]

Examples of time-varying systems

The RC circuit considered earlier if the values of R or C change over time.

y(t) = x(2t) sinec

x(t) = x(2t) but x(t-t0)→ x(2t-t0)

Most physical systems are slowly time-varying due to aging, etc. Hence, they can be considered time-invariant for certain time periods in which its behavior does not change significantly.

**Linear and non linear system**

A system is said to be linear if it satisfies the superposition principle. Superposition principle states that the response to a weighted sum of input signal be equal to the weighted sum of the output corresponding to each of the individual input signal The continuous system is linear if,

F[a1x1(t) + a2x2(t)] = a1y1(t) + a2y2(t)

The discrete system is linear if,

F[a1x1(n) + a2x2(n)] = a1y1(n) + a2y2(n)

Otherwise the system is non linear. A system is called linear if its I/O behavior satisfies the additivity and homogeneity properties:

x1(t)→y1(t) ( x1(t)+x2(t))→(y1(t)+y2(t))

} ⇒

x2(t)→y2(t) (ax1(t)) →(ay1(t))

for any complex constant a.

Equivalently, a system is called linear if its I/O behavior satisfies the superposition property:

x1(t)→y1(t)

}⇒(ax1(t)+bx2(t))→(ay1(t)+by2(t))

x2(t)→y2(t)

where any complex constants a and b.

**Causal and non causal system**

A causal system is one whose output depends upon the present and past input values. If the system depends the future input values, the system is said to be non causal. Eg.for causal system.

Y(t) = x(t) + x(t - 1)

Y(n) = x(n) + x(n - 3)

Ex:- For non causal system,

Y(t) = x(t+3) + x2(t)

Y(n) = x(2n)

A system is called causal or non-anticipative if the output at any time t (or n) depends only on the input at times t or before t (or n or before n); in other words, independent of the input at times after t (or n). All memory less systems are causal. Physical systems where the time is the independent variable are causal. Non-causal systems may arise in applications where the independent variable is not the time such as in the image processing applications.

Examples of causal systems:

y[n] = x[n-1]

Examples of non-causal systems:

x(t) = x(-t)

**Stable and unstable system**

When every bounded input produces bounded output then the system is called as stable system or bounded input bounded output (BIBO stable). Otherwise the system is unstable. A system is called stable if it produces bounded outputs for all bounded inputs Stability in a physical system generally results from the presence of mechanisms that dissipate energy, such as the resistors in a circuit, friction in a mechanical system, etc

## Questions and answers

## What is Applications of DSP ?

Digital signal processing has variety of applications in diverse fields like

- Digital filtering
- Spectral analysis
- Speech processing
- Image processing
- Radar and sonar processing
- Disk and robot control
- Telecommunication
- Consumer electronics
- Biomedical engineering
- Military applications

Digital signal processing has variety of applications in diverse fields like

- Digital filtering
- Spectral analysis
- Speech processing
- Image processing
- Radar and sonar processing
- Disk and robot control
- Telecommunication
- Consumer electronics
- Biomedical engineering
- Military applications

## What is elements of Digital Signal Processing ?

## Anti-Aliasing-Filter

The I/o signal is applying to the antialiasing filter.this is a lowpass filter used to remove the high-frequency noise and Band limit the Signal

The I/o signal is applying to the antialiasing filter.this is a lowpass filter used to remove the high-frequency noise and Band limit the Signal

## Sample&Hold

this device provides the input to the ADC and will be required if the i/o signal was not proper and flute.

this device provides the input to the ADC and will be required if the i/o signal was not proper and flute.

## A/D conveter

this a conveter which converts the Analog S/g to the digital.

this a conveter which converts the Analog S/g to the digital.

## DSP

this gives the better quality signal

this gives the better quality signal

## D/A Conveter

this device reconvenes the signal from digital S/g to the Analog.

this device reconvenes the signal from digital S/g to the Analog.

## Reconstruction filter

this filter is used to construct the signal properly after the signal processing.

this filter is used to construct the signal properly after the signal processing.

## What is Signal processing

Signal processing is the analysis, interpretation, and manipulation of signals like sound, images time-varying measurement values and sensor data etc

For example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others.

Signal processing is the analysis, interpretation, and manipulation of signals like sound, images time-varying measurement values and sensor data etc

For example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others.

## What is Categories of signal processing ?

## Analog signal processing

The analog signal processing is basically, filtering of the signal .

for signals that have not been digitized, as in classical radio, telephone, radar, and television systems.

This involves linear electronic circuits such as passive filters , active filters , additive mixers , integrators and delay lines .

It also involves non-linear circuits such as compandors , multiplicators ( frequency mixers and voltage-controlled amplifiers ), voltage-controlled filters , voltage-controlled oscillators and phase-locked loops .

The analog signal processing is basically, filtering of the signal .

for signals that have not been digitized, as in classical radio, telephone, radar, and television systems.

This involves linear electronic circuits such as passive filters , active filters , additive mixers , integrators and delay lines .

It also involves non-linear circuits such as compandors , multiplicators ( frequency mixers and voltage-controlled amplifiers ), voltage-controlled filters , voltage-controlled oscillators and phase-locked loops .

## Digital signal processing

The digital signal processor consists of anti-aliasing filter, analog to digital converter (ADC), a digital filter represented by the transfer function H(z), a digital to analog converter and a reconstruction filter.

for signals that have been digitized, processing is done by general-purpose computers or by digital circuits such as ASICs , field-programmable gate arrays or specialized digital signal processors (DSP chips).

## Multiple choice questions

1. Which among the following are the stable discrete time systems?

1. y(n) = x(4n)

2. y(n) = x(-n)

3. y(n) = ax (n) + 8

4. y(n) = cos x(n)

a) 1 & 3

b) 2 & 4

c) 1, 3 & 4

d) 1,2,3 & 4

**ANSWER: 1,2,3 & 4**

2. A system is said to be shift invariant only if______

a) a shift in the input signal also results in the corresponding shift in the output

b. a shift in the input signal does not exhibit the corresponding shift in the output

c) a shifting level does not vary in an input as well as output

d) a shifting at input does not affect the output

**ANSWER: a shift in the input signal also results in the corresponding shift in the output**

3. Which among the below specified conditions/cases of discrete time in terms of real constant 'a' , represents the double-sided decaying exponential signal?

a) a > 1

b) 0 < a < 1

c) a < -1

d) -1 < a < 0

**ANSWER: -1 < a < 0**

4. Damped sinusoids are _____

a) sinusoid signals multiplied by growing exponentials

b) sinusoid signals divided by growing exponentials

c) sinusoid signals multiplied by decaying exponentials

d) sinusoid signals divided by decaying exponentials

**ANSWER: sinusoid signals multiplied by decaying exponentials**

5. An amplitude of sinc function that passes through zero at multiple values of an independent variable 'x' ______

a) decreases with an increase in the magnitude of an independent variable (x)

b) increases with an increase in the magnitude of an independent variable (x)

c) always remains constant irrespective of variation in magnitude of' x'

d) cannot be defined

**ANSWER: decreases with an increase in the magnitude of an independent variable (x)**

6. Which condition determines the causality of the LTI system in terms of its impulse response ?

a) Only if the value of an impulse response is zero for all negative values of time

b) Only if the value of an impulse response is unity for all negative values of time

c) Only if the value of an impulse response is infinity for all negative values of time

d) Only if the value of an impulse response is negative for all negative values of time

**ANSWER: Only if the value of an impulse response is zero for all negative values of time**

7. Under which conditions does an initially relaxed system become unstable ?

a) only if bounded input generates unbounded output

b) only if bounded input generates bounded output

c) only if unbounded input generates unbounded output

d) only if unbounded input generates bounded output

**ANSWER: only if bounded input generates unbounded output**

8. An equalizer used to compensate the distortion in the communication system by faithful recovery of an original signal is nothing but an illustration of _________

a) static system

b) dynamic system

c) invertible system

d) none of the above

**ANSWER: invertible system**

9. Which mathematical notation specifies the condition of periodicity for a continuous time signal ?

a) x(t) = x( t +T0)

b) x(n) = x( n+ N)

c) x(t) = e-Î±t

d) None of the above

**ANSWER: x(t) = x( t +T0)**

10. Which property of delta function indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant ?

a)Replication

b) Sampling

c) Scaling

d) Product

**ANSWER: Sampling**

The digital signal processor consists of anti-aliasing filter, analog to digital converter (ADC), a digital filter represented by the transfer function H(z), a digital to analog converter and a reconstruction filter.

for signals that have been digitized, processing is done by general-purpose computers or by digital circuits such as ASICs , field-programmable gate arrays or specialized digital signal processors (DSP chips).

## Multiple choice questions

1. Which among the following are the stable discrete time systems?

1. y(n) = x(4n)

2. y(n) = x(-n)

3. y(n) = ax (n) + 8

4. y(n) = cos x(n)

a) 1 & 3

b) 2 & 4

c) 1, 3 & 4

d) 1,2,3 & 4

**ANSWER: 1,2,3 & 4**

2. A system is said to be shift invariant only if______

a) a shift in the input signal also results in the corresponding shift in the output

b. a shift in the input signal does not exhibit the corresponding shift in the output

c) a shifting level does not vary in an input as well as output

d) a shifting at input does not affect the output

**ANSWER: a shift in the input signal also results in the corresponding shift in the output**

3. Which among the below specified conditions/cases of discrete time in terms of real constant 'a' , represents the double-sided decaying exponential signal?

a) a > 1

b) 0 < a < 1

c) a < -1

d) -1 < a < 0

**ANSWER: -1 < a < 0**

4. Damped sinusoids are _____

a) sinusoid signals multiplied by growing exponentials

b) sinusoid signals divided by growing exponentials

c) sinusoid signals multiplied by decaying exponentials

d) sinusoid signals divided by decaying exponentials

**ANSWER: sinusoid signals multiplied by decaying exponentials**

5. An amplitude of sinc function that passes through zero at multiple values of an independent variable 'x' ______

a) decreases with an increase in the magnitude of an independent variable (x)

b) increases with an increase in the magnitude of an independent variable (x)

c) always remains constant irrespective of variation in magnitude of' x'

d) cannot be defined

**ANSWER: decreases with an increase in the magnitude of an independent variable (x)**

6. Which condition determines the causality of the LTI system in terms of its impulse response ?

a) Only if the value of an impulse response is zero for all negative values of time

b) Only if the value of an impulse response is unity for all negative values of time

c) Only if the value of an impulse response is infinity for all negative values of time

d) Only if the value of an impulse response is negative for all negative values of time

**ANSWER: Only if the value of an impulse response is zero for all negative values of time**

7. Under which conditions does an initially relaxed system become unstable ?

a) only if bounded input generates unbounded output

b) only if bounded input generates bounded output

c) only if unbounded input generates unbounded output

d) only if unbounded input generates bounded output

**ANSWER: only if bounded input generates unbounded output**

8. An equalizer used to compensate the distortion in the communication system by faithful recovery of an original signal is nothing but an illustration of _________

a) static system

b) dynamic system

c) invertible system

d) none of the above

**ANSWER: invertible system**

9. Which mathematical notation specifies the condition of periodicity for a continuous time signal ?

a) x(t) = x( t +T0)

b) x(n) = x( n+ N)

c) x(t) = e-Î±t

d) None of the above

**ANSWER: x(t) = x( t +T0)**

10. Which property of delta function indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant ?

a)Replication

b) Sampling

c) Scaling

d) Product

**ANSWER: Sampling**

## Basic elements of Digital Signal Processing (DSP)

## Classification of Signals

1. Which of the following is the odd component of the signal x(t)=e(jt)?

a) cost

b) j*sint

c) j*cost

d) sint

**Answer: j*sint**

2. The deflection voltage of an oscilloscope is a ‘deterministic’ signal.

a) True

b) False

**Answer: True**

3. The even part of a signal x(t) is?

a) x(t)+x(-t)

b) x(t)-x(-t)

c) (1/2)*(x(t)+x(-t))

d) (1/2)*(x(t)-x(-t))

**Answer: (1/2)*(x(t)+x(-t))**

4. Which of the following is done to convert a continuous time signal into discrete time signal?

a) Modulating

b) Sampling

c) Differentiating

d) Integrating

**Answer: Sampling**

5. For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to ___________

a) x(-t)

b) x(mT)

c) x(mt)

d) x(t)

**Answer: x(t)**

6. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x1(t)+x2(t) to be periodic?

a) T1+T2

b) T1-T2

c) T1/T2

d) T1*T2

**Answer: T1/T2**

7. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Then the fundamental period of x(t)=x1(t)+x2(t) is?

a) LCM of T1 and T2

b) HCF of T1and T2

c) Product of T1 and T2

d) Ratio of T1 to T2

**Answer: LCM of T1 and T2**

8. All energy signals will have an average power of ___________

a) Infinite

b) Zero

c) Positive

d) Cannot be calculated

**Answer: Zero**

9. x(t) or x(n) is defined to be an energy signal, if and only if the total energy content of the signal is a ___________

a) Finite quantity

b) Infinite

c) Zero

d) None of the mentioned

**Answer: Finite quantity**

10. What is the period of cos2t+sin3t?

a) pi

b) 2*pi

c) 3*pi

d) 4*pi

**Answer: 2*pi**

1. Which of the following is the odd component of the signal x(t)=e(jt)?

a) cost

b) j*sint

c) j*cost

d) sint**Answer: j*sint**

2. The deflection voltage of an oscilloscope is a ‘deterministic’ signal.

a) True

b) False**Answer: True**

3. The even part of a signal x(t) is?

a) x(t)+x(-t)

b) x(t)-x(-t)

c) (1/2)*(x(t)+x(-t))

d) (1/2)*(x(t)-x(-t))**Answer: (1/2)*(x(t)+x(-t))**

4. Which of the following is done to convert a continuous time signal into discrete time signal?

a) Modulating

b) Sampling

c) Differentiating

d) Integrating**Answer: Sampling**

5. For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to ___________

a) x(-t)

b) x(mT)

c) x(mt)

d) x(t)**Answer: x(t)**

6. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x1(t)+x2(t) to be periodic?

a) T1+T2

b) T1-T2

c) T1/T2

d) T1*T2**Answer: T1/T2**

7. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Then the fundamental period of x(t)=x1(t)+x2(t) is?

a) LCM of T1 and T2

b) HCF of T1and T2

c) Product of T1 and T2

d) Ratio of T1 to T2**Answer: LCM of T1 and T2**

8. All energy signals will have an average power of ___________

a) Infinite

b) Zero

c) Positive

d) Cannot be calculated**Answer: Zero**

9. x(t) or x(n) is defined to be an energy signal, if and only if the total energy content of the signal is a ___________

a) Finite quantity

b) Infinite

c) Zero

d) None of the mentioned**Answer: Finite quantity**

10. What is the period of cos2t+sin3t?

a) pi

b) 2*pi

c) 3*pi

d) 4*pi**Answer: 2*pi**

## signals, Systems and Signal Processing

## 1. The interface between an analog signal and a digital processor is

a) D/A converter

b) A/D converter

c) Modulator

d) Demodulator

**Answer: A/D converter**2. Which of the following conditions made digital signal processing more advantageous over analog signal processing?

a) Flexibility

b) Accuracy

c) Storage

d) All of the mentioned

**Answer: All of the mentioned**

3. Which property does y(t)=x(1-t) exhibit?

a) Time scaling

b) Time shifting

c) Reflecting

d) Time shifting and reflecting

**Answer: Time shifting and reflecting**

4. If x(n)=(0,1,2,3,3,0,0,0) then x(2n) is?

a) (0,2,4,6,6,0,0,0)

b) (0,1,2,3,3,0,0,0)

c) (0,2,3,0,0,0,0,0)

d) None of the mentioned

**Answer: (0,2,3,0,0,0,0,0)**

5. If x(n)=(0,0,1,2,3,4,0,0) then x(n-2) is?

a) (0,0,2,4,6,8,0,0)

b) (0,0,1,2,3,4,0,0)

c) (1,2,3,4,0,0,0,0)

d) (0,0,0,0,1,2,3,4)

**Answer: (0,0,0,0,1,2,3,4)**

6. If x(n)=(0,0,1,1,1,1,1,0) then x(3n+1) is?

a) (0,1,0,0,0,0,0,0)

b) (0,0,1,1,1,1,0,0)

c) (1,1,0,0,0,0,0,0)

d) None of the mentioned

**Answer: (0,1,0,0,0,0,0,0)**

7. If a signal x(t) is processed through a system to obtain the signal (x(t)2), then the system is said to be ____________

a) Linear

b) Non-linear

c) Exponential

d) None of the mentioned

**Answer: Non-linear**

8. What are the important block(s) required to process an input analog signal to get an output analog signal?

a) A/D converter

b) Digital signal processor

c) D/A converter

d) All of the mentioned

**Answer: All of the mentioned**

9. Which of the following block is not required in digital processing of a RADAR signal?

a) A/D converter

b) D/A converter

c) DSP

d) All of the mentioned

**Answer: D/A converter**

10. Which of the following wave is known as “amplitude modulated wave” of x(t)?

a) C.x(t) (where C is a constant)

b) x(t)+y(t)

c) x(t).y(t)

d) dx(t)/dt

**Answer: x(t).y(t)**

11. What is the physical device that performs an operation on the signal?

a) Signal source

b) System

c) Medium

d) None of the mentioned

**Answer: System**

12. Which of the following is common independent variable for speech signal, EEG and ECG?

a) Time

b) Spatial coordinates

c) Pressure

d) None of the mentioned

**Answer: Time**

a) D/A converter

b) A/D converter

c) Modulator

d) Demodulator

**Answer: A/D converter**

2. Which of the following conditions made digital signal processing more advantageous over analog signal processing?

a) Flexibility

b) Accuracy

c) Storage

d) All of the mentioned**Answer: All of the mentioned**

3. Which property does y(t)=x(1-t) exhibit?

a) Time scaling

b) Time shifting

c) Reflecting

d) Time shifting and reflecting**Answer: Time shifting and reflecting**

4. If x(n)=(0,1,2,3,3,0,0,0) then x(2n) is?

a) (0,2,4,6,6,0,0,0)

b) (0,1,2,3,3,0,0,0)

c) (0,2,3,0,0,0,0,0)

d) None of the mentioned**Answer: (0,2,3,0,0,0,0,0)**

5. If x(n)=(0,0,1,2,3,4,0,0) then x(n-2) is?

a) (0,0,2,4,6,8,0,0)

b) (0,0,1,2,3,4,0,0)

c) (1,2,3,4,0,0,0,0)

d) (0,0,0,0,1,2,3,4)**Answer: (0,0,0,0,1,2,3,4)**

6. If x(n)=(0,0,1,1,1,1,1,0) then x(3n+1) is?

a) (0,1,0,0,0,0,0,0)

b) (0,0,1,1,1,1,0,0)

c) (1,1,0,0,0,0,0,0)

d) None of the mentioned**Answer: (0,1,0,0,0,0,0,0)**

7. If a signal x(t) is processed through a system to obtain the signal (x(t)2), then the system is said to be ____________

a) Linear

b) Non-linear

c) Exponential

d) None of the mentioned**Answer: Non-linear**

8. What are the important block(s) required to process an input analog signal to get an output analog signal?

a) A/D converter

b) Digital signal processor

c) D/A converter

d) All of the mentioned**Answer: All of the mentioned**

9. Which of the following block is not required in digital processing of a RADAR signal?

a) A/D converter

b) D/A converter

c) DSP

d) All of the mentioned**Answer: D/A converter**

10. Which of the following wave is known as “amplitude modulated wave” of x(t)?

a) C.x(t) (where C is a constant)

b) x(t)+y(t)

c) x(t).y(t)

d) dx(t)/dt**Answer: x(t).y(t)**

11. What is the physical device that performs an operation on the signal?

a) Signal source

b) System

c) Medium

d) None of the mentioned**Answer: System**

12. Which of the following is common independent variable for speech signal, EEG and ECG?

a) Time

b) Spatial coordinates

c) Pressure

d) None of the mentioned**Answer: Time**

## analog to digital conversion (ADC)

1. Which of the following should be done in order to convert a continuous-time signal to a discrete-time signal?

a) Sampling

b) Differentiating

c) Integrating

d) None of the mentioned

**Answer: Sampling**

2. The process of converting discrete-time continuous valued signal into discrete-time discrete valued (digital) signal is known as ____________

a) Sampling

b) Quantization

c) Coding

d) None of the mentioned

**Answer: Quantization**

3. The difference between the unquantized x(n) and quantized xq(n) is known as ___________

a) Quantization coefficient

b) Quantization ratio

c) Quantization factor

d) Quantization error

**Answer: Quantization error**

4. Which of the following is a digital-to-analog conversion process?

a) Staircase approximation

b) Linear interpolation

c) Quadratic interpolation

d) All of the mentioned

**Answer: All of the mentioned**

5. The relation between analog frequency ‘F’ and digital frequency ‘f’ is?

a) F=f*T(where T is sampling period)

b) f=F*T

c) No relation

d) None of the mentioned

**Answer: f=F*T**

6. What is output signal when a signal x(t)=cos(2**pi**40*t) is sampled with a sampling frequency of 20Hz?

a) cos(pi*n)

b) cos(2**pi**n)

c) cos(4**pi**n)

d) cos(8**pi**n)

**Answer: cos(4****pi**n)

7. If ‘F’ is the frequency of the analog signal, then what is the minimum sampling rate required to avoid aliasing?

a) F

b) 2F

c) 3F

d) 4F

**Answer: F**

8. What is the nyquist rate of the signal x(t)=3cos(50**pi**t)+10sin(300**pi**t)-cos(100**pi**t)?

a) 50Hz

b) 100Hz

c) 200Hz

d) 300Hz

**Answer: 300Hz**

9. What is the discrete-time signal obtained after sampling the analog signal x(t)=cos(2000**pi**t)+sin(5000**pi**t) at a sampling rate of 5000 samples/sec?

a) cos(2.5**pi**n)+sin(pi*n)

b) cos(0.4**pi**n)+sin(pi*n)

c) cos(2000**pi**n)+sin(5000**pi**n)

d) none of the mentioned

**Answer: cos(0.4****pi**n)+sin(pi*n)

10. If the sampling rate Fs satisfies the sampling theorem, then the relation between quantization errors of analog signal(eq(t)) and discrete-time signal(eq(n)) is?

a) eq(t)=eq(n)

b) eq(t)<eq(n)

c) eq(t)>eq(n)

d) not related

**Answer: eq(t)=eq(n)**

11. The quality of output signal from A/D converter is measured in terms of ___________

a) Quantization error

b) Quantization to signal noise ratio

c) Signal to quantization noise ratio

d) Conversion constant

**Answer: Signal to quantization noise ratio**

12. Which bit coder is required to code a signal with 16 levels?

a) 8 bit

b) 4 bit

c) 2 bit

d) 1 bit

**Answer: 4 bit**

1. Which of the following should be done in order to convert a continuous-time signal to a discrete-time signal?

a) Sampling

b) Differentiating

c) Integrating

d) None of the mentioned**Answer: Sampling**

2. The process of converting discrete-time continuous valued signal into discrete-time discrete valued (digital) signal is known as ____________

a) Sampling

b) Quantization

c) Coding

d) None of the mentioned**Answer: Quantization**

3. The difference between the unquantized x(n) and quantized xq(n) is known as ___________

a) Quantization coefficient

b) Quantization ratio

c) Quantization factor

d) Quantization error**Answer: Quantization error**

4. Which of the following is a digital-to-analog conversion process?

a) Staircase approximation

b) Linear interpolation

c) Quadratic interpolation

d) All of the mentioned**Answer: All of the mentioned**

5. The relation between analog frequency ‘F’ and digital frequency ‘f’ is?

a) F=f*T(where T is sampling period)

b) f=F*T

c) No relation

d) None of the mentioned**Answer: f=F*T**

6. What is output signal when a signal x(t)=cos(2**pi**40*t) is sampled with a sampling frequency of 20Hz?

a) cos(pi*n)

b) cos(2**pi**n)

c) cos(4**pi**n)

d) cos(8**pi**n)**Answer: cos(4* pi*n)**

7. If ‘F’ is the frequency of the analog signal, then what is the minimum sampling rate required to avoid aliasing?

a) F

b) 2F

c) 3F

d) 4F**Answer: F**

8. What is the nyquist rate of the signal x(t)=3cos(50**pi**t)+10sin(300**pi**t)-cos(100**pi**t)?

a) 50Hz

b) 100Hz

c) 200Hz

d) 300Hz**Answer: 300Hz**

9. What is the discrete-time signal obtained after sampling the analog signal x(t)=cos(2000**pi**t)+sin(5000**pi**t) at a sampling rate of 5000 samples/sec?

a) cos(2.5**pi**n)+sin(pi*n)

b) cos(0.4**pi**n)+sin(pi*n)

c) cos(2000**pi**n)+sin(5000**pi**n)

d) none of the mentioned**Answer: cos(0.4* pi*n)+sin(pi*n)**

10. If the sampling rate Fs satisfies the sampling theorem, then the relation between quantization errors of analog signal(eq(t)) and discrete-time signal(eq(n)) is?

a) eq(t)=eq(n)

b) eq(t)<eq(n)

c) eq(t)>eq(n)

d) not related**Answer: eq(t)=eq(n)**

11. The quality of output signal from A/D converter is measured in terms of ___________

a) Quantization error

b) Quantization to signal noise ratio

c) Signal to quantization noise ratio

d) Conversion constant**Answer: Signal to quantization noise ratio**

12. Which bit coder is required to code a signal with 16 levels?

a) 8 bit

b) 4 bit

c) 2 bit

d) 1 bit**Answer: 4 bit**

## Discrete-time signals

1. Determine the discrete-time signal: x(n)=1 for n≥0 and x(n)=0 for n<0

a) Unit ramp sequence

b) Unit impulse sequence

c) Exponential sequence

d) Unit step sequence

**Answer: Unit step sequence**

2. What is the time period of the function x[n] = exp(jwn)?

a) pi/2w

b) pi/w

c) 2pi/w

d) 4pi/w

**Answer: 2pi/w**

3. What is the nature of the following function: y[n] = y[n-1] + x[n]?

a) Integrator

b) Differentiator

c) Subtractor

d) Accumulator

**Answer: Accumulator**

4. Is the above function defined, causal in nature?

a) True

b) False

**Answer: True**

5. Is the function y[n] = x[n-1] – x[n-4] memoryless?

a) True

b) False

**Answer: False**

6. Is the function y[n] = x[n-1] – x[n-56] causal?

a) The system is non causal

b) The system is causal

c) Both causal and non causal

d) None of the mentioned

**Answer: The system is causal**

7. Is the function y[n] = y[n-1] + x[n] stable in nature?

a) It is stable

b) It is unstable

c) Both stable and unstable

d) None of the mentioned

**Answer: It is stable**

8. If n tends to infinity, is the accumulator function a stable one?

a) The function is marginally stable

b) The function is stable

c) The function is unstable

d) None of the mentioned

**Answer: The function is unstable**

9. We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n], is z[n] stable?

a) Yes

b) No

**Answer: Yes**

10. We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n]. Is z[n] a causal system?

a) No

b) Yes

**Answer: Yes**

11. Discrete-time signals are ________________

a) Continuous in amplitude and continuous in time

b) Continuous in amplitude and discrete in time

c) Discrete in amplitude and discrete in time

d) Discrete in amplitude and continuous in time

**Answer: Continuous in amplitude and discrete in time**

12. Is the function y[n] = sin(x[n]) periodic or not?

a) True

b) False

**Answer: False**

13. Determine the value of the summation: ∑^∞ n= -∞^Î´(n-1)sin2n.

a) 1

b) 0

c) sin2

d) sin4

**Answer: sin2**

14. Determine the value of the summation: ∑^∞ n= -∞^Î´(n+3)(n2+n).

a) 3

b) 6

c) 9

d) 12

**Answer: 6**

15. Determine the product of two signals: x1 (n) = {2,1,1.5,3}; x2 (n) = { 1,1.5,0,2}.

a) {2,1.5,0,6}

b) {2,1.5,6,0}

c) {2,0,1.5,6}

d) {2,1.5,0,3}

**Answer: {2,1.5,0,6}**

1. Determine the discrete-time signal: x(n)=1 for n≥0 and x(n)=0 for n<0

a) Unit ramp sequence

b) Unit impulse sequence

c) Exponential sequence

d) Unit step sequence**Answer: Unit step sequence**

2. What is the time period of the function x[n] = exp(jwn)?

a) pi/2w

b) pi/w

c) 2pi/w

d) 4pi/w**Answer: 2pi/w**

3. What is the nature of the following function: y[n] = y[n-1] + x[n]?

a) Integrator

b) Differentiator

c) Subtractor

d) Accumulator**Answer: Accumulator**

4. Is the above function defined, causal in nature?

a) True

b) False**Answer: True**

5. Is the function y[n] = x[n-1] – x[n-4] memoryless?

a) True

b) False**Answer: False**

6. Is the function y[n] = x[n-1] – x[n-56] causal?

a) The system is non causal

b) The system is causal

c) Both causal and non causal

d) None of the mentioned**Answer: The system is causal**

7. Is the function y[n] = y[n-1] + x[n] stable in nature?

a) It is stable

b) It is unstable

c) Both stable and unstable

d) None of the mentioned**Answer: It is stable**

8. If n tends to infinity, is the accumulator function a stable one?

a) The function is marginally stable

b) The function is stable

c) The function is unstable

d) None of the mentioned**Answer: The function is unstable**

9. We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n], is z[n] stable?

a) Yes

b) No**Answer: Yes**

10. We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n]. Is z[n] a causal system?

a) No

b) Yes**Answer: Yes**

11. Discrete-time signals are ________________

a) Continuous in amplitude and continuous in time

b) Continuous in amplitude and discrete in time

c) Discrete in amplitude and discrete in time

d) Discrete in amplitude and continuous in time**Answer: Continuous in amplitude and discrete in time**

12. Is the function y[n] = sin(x[n]) periodic or not?

a) True

b) False**Answer: False**

13. Determine the value of the summation: ∑^∞ n= -∞^Î´(n-1)sin2n.

a) 1

b) 0

c) sin2

d) sin4**Answer: sin2**

14. Determine the value of the summation: ∑^∞ n= -∞^Î´(n+3)(n2+n).

a) 3

b) 6

c) 9

d) 12**Answer: 6**

15. Determine the product of two signals: x1 (n) = {2,1,1.5,3}; x2 (n) = { 1,1.5,0,2}.

a) {2,1.5,0,6}

b) {2,1.5,6,0}

c) {2,0,1.5,6}

d) {2,1.5,0,3}**Answer: {2,1.5,0,6}**

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