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

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

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

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= -∞^δ(n-1)sin2n.
a) 1
b) 0
c) sin2
d) sin4
Answer: sin2

14. Determine the value of the summation: ∑^∞ n= -∞^δ(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}