DIGITAL-SIGNAL PROCESSING (DSP)
UNIT I: Introduction to DSP
PART-A:
1. Define DSP and give the Merits, Demerits and Applications?
2. Justify whether the following system is Time-Invariant or not
(i).y(n)=sin(x(n)) (ii).y(n)=2x(n-1)+5
3. Justify the stability of the system whose Impulse Response is h(n)=(1/2) u(n).
4. List the various Applications of Z-Transform?
5. Design the Flow Graph of Linear Phase FIR System?
6. Design the Flow Graph of a Realization of IIR System for Cascade and Parallel Form.
7. Explain different types of discrete time signals and sequence representations.
8. Explain graphically elementary discrete time signals.
9. Explain classification of discrete time signals.
10. Define signals and systems.
11. Explain advantages & disadvantages of DSP over ASP.
12. Explain the classification of discrete time systems with their relevant examples.
13. Explain the terms Causal & non-causal systems, Linear & Non-linear systems
Time variant & Time invariant systems, Stability & Unstability
14. Determine the DSP system y[n]=log10x[n] is
i) Linear ii) Causality iii) Stability iv) Time-variant whether above statement satisfies or
not.
15. Explain the methods of frequency domain representation of discrete time signals.
16. Find the (i)impulse response(ii) frequency response(iii) magnitude response & (iv)phase
response of the given second order system y[n]-y[n-1]+ 3/16y[n-2]=x[n]- 1/2x[n-1].
17. Define terms
i) Energy & power signals
ii) Periodic & a periodic signals
c) Symmetric & anti-symmetric signals
18. Determine the values of power & energy of given signal. Find whether the signals are
power or neither energy nor power signals.
i) x[n]=e j(/2n+/4) ii)x[n]= sin(/4n) iii) x[n]=(1/3)n u[n]
19. Check the following system for linearity, causality, time invariance & stability using
appropriate test
i) y[n] = nex(n) ii) y[n] = an cos(2n N) iii) y[n] = x[-n] iv) y[n] =
log10x(n)
PART-B:
1. Solve the following difference equation
(a).y(n)=0.7y(n-1)-0.1y(n-2)+2x(n)-x(n-2),the input x(n) is the Unit Sample
(b).y(n)-4y(n-1)+4y(n-2)=x(n)-x(n-1),input is x(n)=(-1) u(n) and initial conditions y(-
1)=y(-2)=1
2. (a).Find the Impulse Response and Frequency Response of the filter defined by
y(n)=x(n)+by(n-1)
(b).The Impulse Response of a LTI system is given by h(n)=(0.6) u(n).Find the
Frequency Response.
3. (a).Find the response for the following system y(n)-y(n-1)+6y(n-2)=x(n)where x(n)=n
(b).A LTI system is described by the following difference equation, y(n)=ay(n-
1)+bx(n).Find the Impulse Response, Magnitude function and Phase function.
4. (a).Find the Impulse Response of the system described by the difference equation y(n)-
3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z-Transform
(b).An LTI system is described by the equation y(n)=x(n)+0.81x(n-1)-0.81x(n-2)-0.45y(n
2).Determine Transfer function and sketch the Poles and Zeros on the Z-plane.
5. (a).Find the Frequency Response, Magnitude Response and Phase Response For the
system given by, y(n)-(3/4)y(n-1)+(1/8)y(n-2)=x(n)-x(n-1)
(b).The Impulse Response of an LTI system is given by h(n)=(r) cos(wOn)u(n).Find the
Frequency Response of the system.
6. (a).Design Direct Form-I & II IIR Realization Structures in detail with necessary Flow
Graphs.
(b).Find the digital network in Direct and Transposed form for the system described by
the difference equation y(n)=x(n)+0.5x(n-1)+0.4x(n-2)-0.6y(n-1)-0.7y(n-2).
UNIT 2: DFS and Fast Fourier Transform
PART-A:
1. Define the DFS Representation of periodic Sequences?
2. List and explain the Properties of DFS?
3. List and explain the Properties of DFT?
4. Define FFT? Calculate the number of multiplications needed in the calculation of DFT
using FFT Algorithm with 32- point sequence.
5. Comparison between Radix-2 DIT-FFT and DIF-FFT Algorithms?
6. Sketch the basic Butterfly Structure for Radix-2 DIT-FFT and DIF-FFT Algorithms?
7. Determine the 8-point DFT of the sequence x(n) = {1, 1, 1, 1, 1, 1, 0, 0}.
8. Explain any four properties of DFT.
9. Prove DFT [x(n) ej2lnn/N] = X ((k-l))N
10. Compute the DFT of x(n) {1, 0, 0, 0} & Compare with Xd(w).
11. Define DFT of a sequence x(n).
PART-B:
1. (a).Compute the 8-Point DFT of the sequence x(n)={1,1,1,1,1,1,0,0}
(b).Compute the IDFT of the sequence X(K)={5,0,1-j,0,1,0,1+j,0}
2. Compute the Linear Convolution of the following two sequences using DFT& IDFT
(i).x(n)={2,1,2,1} and h(n)={1,2,3,4} (ii).x(n)={1,0.5,0} and h(n)={0.5,1}
3. Find the output y(n) of a filter whose Impulse Response is h(n)={1,2} and input
x(n)={1,2,-1,2,3,-2,-3,-1,1,1,2,-1} by using (i).Overlap-Add method (ii).Overlap-
Save method.
4. An 8-Point sequence is given by x(n)={2,2,2,2,1,1,1,1}.Compute 8-Point DFT of
x(n) by (i).Radx-2 DIT-FFT Algorithm (ii). Radx-2 DIF-FFT Algorithm
5. Design the Butterfly line Diagram for 8-Point FFT calculation and briefly explain
using (i).Radx-2 DIT-FFT Algorithm (ii). Radx-2 DIF-FFT Algorithm
6. .An 8-Point sequence is given by X(K)={4,0,0,0,4,0,0,0}.Compute 8-Point IDFT of
X(K) by (i).Radx-2 DIT-FFT Algorithm (ii). Radx-2 DIF-FFT Algorithm.
7. If x(n) is a periodic sequence with periodic N, also periodic with a period 2N, X1(k)
denotes the discrete fourier series coefficient of x(n) with period N and X2(k) denote the
discrete fourier series coefficient of x(n) with period 2N. Determine X2(k) in terms of
X1(k).
8. Prove x*(-n)x*((-k))N RN(k).
a) Compute the circular convolution of the sequences
b) x1(n) = {1, 2, 0, 1} & x2(n) = {2, 2, 1, 1} using DFT approach.
c) Define DFT and give three properties of DFT.
d) Consider a sequence x(n) = {2, -1, 1, 1}. Compute its DFT and compare it with
its DTFT.
e) Distinguish between DFT and DTFT.
9. If x1(n) and x2(n) are to finite sequences, derive linear convolution of these sequences
using circular convolution.
10. Derive relationship between Z-Transforms & DFT.
11. What is padding with zeros explain with example and Explain the effect of padding a
sequence of length N with L zeros of frequency reduction.
12. Determine the output response y(n) if h(n) = {1, 1, 1} & x(n) = {1, 2, 3, 1} by using
13. Linear convolution ii) Circular Convolution iii) Circular Convolution with zero padding.
14. Find the circular convolution of two finite duration sequences
15. x1(n) = {1, -1, -2, 3, -1}; x2(n) = {1, 2, 3} using
16. i) Concentric circle method ii) Matrix method.
a) Find the DFT of a sequence x(n) = {1, 1, 0, 0}
b) Find the IDFT of a sequence X(k) = {5, 0, 1-j, 0, 1, 0, 1+j, 0}
UNIT 3: IIR Digital Filters
PART-A:
1. How one can design digital filters from Analog Filters?
2. Find the order of the LPF for Butterworth Approximation, for 3dB attenuation at 500Hz
and an attenuation of 40dB at 1000Hz.
3. Realize the system with difference equation,y(n)=(3/4)y(n-1)-(1/8)y(n-2)+x(n)+(1/3)x(n-
1) in Cascade Form.
PART-B:
1. (a)Compare Butterworth and Chebyshev Filters
(b).Find the order of LPF if it has pass band attenuation of -3dB a at800rad/sec and stop
band attenuation of -10dB at 1800rad/sec
2. Design and Explain the Analog Filter using Butterworth Approximation
3. Design and Explain the Analog Filter using Chebyshev Approximation
