FIR Filters 1. What is the value of h(M-1/2) if the unit sample response is anti-symmetric? a) 0 b) 1 c) -1 d) None of the mentioned Answer: 0 2. Which of the following condition should the unit sample response of a FIR filter satisfy to have a linear phase? a) h(M-1-n) n=0,1,2…M-1 b) ±h(M-1-n) n=0,1,2…M-1 c) -h(M-1-n) n=0,1,2…M-1 d) None of the mentioned Answer: ±h(M-1-n) n=0,1,2…M-1 3. If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs. a) True b) False Answer: False 4. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter. a) True b) False Answer: True 5. The anti-symmetric condition is not used in the design of low pass linear phase FIR filter. a) True b) False Answer: True 6. The roots of the polynomial H(z) are identical to the roots of the polynomial   H(z -1 ). a) True b) False Answer: True 7. The roots of the equation

  Transfer Function 1. A linear system at rest is subject to an input signal r(t)=1-e -t . The response of the system for t>0 is given by c(t)=1-e -2t . The transfer function of the system is: a) (s+2)/(s+1) b) (s+1)/(s+2) c) 2(s+1)/(s+2) d) (s+1)/2(s+2) Answer: 2(s+1)/(s+2) 2. In continuous data systems : a) Data may be continuous function of time at all points in the system b) Data is necessarily a continuous function of time at all points in the system c) Data is continuous at the inputs and output parts of the system but not necessarily during intermediate processing of the data d) Only the reference signal is continuous function of time Answer: Data is necessarily a continuous function of time at all points in the system 3. In regenerating the feedback, the transfer function is given by a) C(s)/R(s)=G(s)/1+G(s)H(s) b) C(s)/R(s)=G(s)H(s)/1-G(s)H(s) c) C(s)/R(s)=G(s)/1+G(s)H(s) d) C(s)/R(s)=G(s)/1-G(s)H(s) Answer: C(s)/R(s)=G(s)/1-G(s)H(s) 4. A control system w

  Z transform 1. What is the set of all values of z for which X(z) attains a finite value? a) Radius of convergence b) Radius of divergence c) Feasible solution d) None of the mentioned Answer: Radius of convergence 2. Is the discrete time LTI system with impulse response h(n)=a n (n) (|a| < 1) BIBO stable? a) True b) False Answer: True 3. What is the ROC of a causal infinite length sequence? a) |z|<r 1 b) |z|>r 1 c) r 2 <|z|<r 1 d) None of the mentioned Answer: |z|>r 1 4. The Z-Transform X(z) of a discrete time signal x(n) is defined as ____________ a)   ∑ ∞ k=-∞   x(n)z n b)   ∑ ∞ k=-∞   x(n)z -n c)   ∑ ∞ k=0 x(n)z n d) None of the mentioned Answer:   ∑ ∞ k=-∞   x(n)z -n 5. What is the z-transform of the following finite duration signal? x(n)={2, 4, 5, 7, 0, 1}?                    ↑ a) 2 + 4z + 5z 2  + 7z 3  + z 4 b) 2 + 4z + 5z 2  + 7z 3  + z 5 c) 2 + 4z -1  + 5z -2  + 7z -3  + z -5 d) 2z 2  + 4z + 5 +7z -1  + z -3 Answer: 2z 2  + 4z +

  Discrete Time Systems 1. Comment on the causality of the following discrete time system: y[n] = x[-n]. a) Causal b) Non causal c) Both Casual and Non casual d) None of the mentioned Answer: Non causal 2. Is the function y[n] = cos(x[n]) periodic or not? a) True b) False Answer: True 3. Consider the system y[n] = 2x[n] + 5. Is the function linear? a) Yes b) No Answer: No 4. If n tends to infinity, is the accumulator function an unstable one? a) The function is marginally stable b) The function is unstable c) The function is stable d) None of the mentioned Answer: The function is unstable 5. Comment on the causality of the discrete time system: y[n] = x[n+3]. a) Causal b) Non Causal c) Anti Causal d) None of the mentioned Answer: Anti Causal 6.Comment on the time invariance of the following discrete system: y[n] = x[2n+4]. a) Time invariant b) Time variant c) Both Time variant and Time invariant d) None of the mentioned Answer: Time variant 7. How is a

Linear convolution  Read more 1 .Which of the following is a correct expression for Impulse response? A) x[n] = ∑ ∞ k=-∞  x[k]δ[n-k] B) x[n] = ∑ ∞ k=-∞  x[k]δ[nk] C) x[n] = ∑ ∞ k=-∞  x[k]δ[k] D) x[n] = ∑ ∞ k=-∞  x[k]δ[n] Answer:  x[n] = ∑ ∞ k=-∞  x[k]δ[n-k] 2.  The convolution sum is given by _____ equation. A) x[n]*h[n] = ∑ ∞ k=-∞  x[k]h[n-k] B) x[n]*h[n] = ∑ ∞ k=-∞  x[n]h[n-k] C) x[n]*h[n] = ∑ ∞ k=-∞  x[k]h[nk] D) x[n]*h[n] = ∑ ∞ k=-∞  x[k]h[k] Answer:  x[n]*h[n] = ∑ ∞ k=-∞  x[k]h[n-k]. 3. Impulse response is the output of ______ system due to impulse input applied at time=0? A) Linear B) Time varying C) Time invariant D) Linear and time invariant Answer: Linear and time invariant 4. Which of the following is correct regarding to impulse signal? A) x[n]δ[n] = x[0]δ[n] B) x[n]δ[n] = δ[n] C) x[n]δ[n] = x[n] D) x[n]δ[n] = x[0] Answer: x[n]δ[n] = x[0]δ[n] 5. Weighted superposition of time-shifted impulse responses is termed as _______ for discrete-time signals. A) Convoluti

  Causality And Stability Of Discrete Time Systems Discrete Time Systems Discrete time systems A discrete-time system is a system that maps an input sequence with an output sequence  y[n] = T {x[n]} A discrete-time system is a device or algorithm that, according to some well-defined rule, operates on a discrete-time signal called the input signal or excitation to produce another discrete-time signal called the output signal or response. Mathematically speaking, a system is also a function. The input signal x[n] is transformed by the system into a signal y[n], which we express mathematically as y[·] = T {x[·]} or y[n] = T {x[·]}[n] or x[·]  T→ y[·]  The notation y[n] = T {x[n]} is mathematically vague. The reader must understand that in general y[n] is a function of the entire sequence {x[n]}, not just the single time point x[n]. Input Signal x[n]→ Discrete-time system → Output Signal y[n] Causality If a discrete-time system is causal, then the current output sample depends only on the

  Linear Convolution Linear convolution is a mathematical operation done to calculate the output of any Linear-Time Invariant (LTI) system given its input and impulse response. It is applicable for both continuous and discrete-time signals. We can represent Linear Convolution as y(n)=x(n)*h(n) Here, y(n) is the output (also known as convolution sum). x(n) is the input signal, and h(n) is the impulse response of the LTI system. In linear convolution, both the sequences (input and impulse response) may or may not be of equal sizes. That is, they may or may not have the same number of samples. Thus the output, too, may or may not have the same number of samples as any of the inputs. For example:- consider the following signals x(n): [1,2,3] h(n): [1,2,3,4,5] As you can see, the number of samples in the input and Impulse response signals is not the same. Still, linear convolution is possible. Here’s how you calculate the number of samples in the output of linear convolution. L

  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 Digital Signal Processing is the process of representing signals in a discrete mathematical sequence of numbers and analyzing, modifying, and extracting the information contained in the signal by carrying out algorithmic operations and processing on the si