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Answer All The Questions Marks

1. This document contains questions about digital signal processing topics including filtering, discrete Fourier transforms, filter design, and realization of difference equations. 2. It asks to determine impulse responses, perform DFTs and IDFTs, compute filter responses using convolution, design low pass and Butterworth filters, and obtain different realizations for filters including direct form, cascade, and parallel structures. 3. It also contains questions about roundoff noise analysis, downsampling and upsampling, and determining the output of a system from a signal flow graph.

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Paramesh Waran
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154 views2 pages

Answer All The Questions Marks

1. This document contains questions about digital signal processing topics including filtering, discrete Fourier transforms, filter design, and realization of difference equations. 2. It asks to determine impulse responses, perform DFTs and IDFTs, compute filter responses using convolution, design low pass and Butterworth filters, and obtain different realizations for filters including direct form, cascade, and parallel structures. 3. It also contains questions about roundoff noise analysis, downsampling and upsampling, and determining the output of a system from a signal flow graph.

Uploaded by

Paramesh Waran
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ANSWER ALL THE QUESTIONS MARKS

1.a) Determine frequncy response, impulse response for difference (6)


equation y(n)-(3/4)y(n-1)+(1/8)y(n-2)=x(n)

b)Given X(k) = {10, -2+2j, -2, -2-2j} (4)


find x(n) using IFFT- DIF algorithm.

c)By means of DFT and IDFT , Perform circular convolution for impulse (10)
response h(n)={1,2,3,4}to the input sequence x(n)={1,2,2,1}

2.An 8-point discrete time sequence is given by x(n) = {2,2,2,2,1,1,1,1}. (10)


Compute the 8-point DFT of x(n) using radix-2 DIT- FFT algorithm.

c) Obtain direct form and linear phase realization for


(6)
h(n)={0.225, 0.8, 0.75, 0.5, 0.75, 0.8, 0.225}

d) Obtain cascade realization for FIR filter (4)


y(n)-(3/4)y(n-1)+(1/8)y(n-2)=x(n)

3.a)Design a low pass filter with a frequency response (10)


Hd( ejω ) = e-3jw for -π /4 ≤ ω ≤ π /4
= 0 for π /4 | ω | ≤ π
Using Hanning window & N = 7.

b)Design a Butterworth filter using the bilinear method for the following (10)
specifications .Assume T=1sec
0.9 ≤ | H( ejω ) | ≤ 1 ; 0 ≤ ω ≤ π/2
jω
| H( e ) | ≤ 0.2 ; 3π/4 ≤ ω ≤ π

4. a)Draw the direct form I, II, cascade realization


y(n)= (3/4)y(n-1)-(1/8)y(n-2)+x(n)+(1/3)x(n-1 )

b) Obtain parallel realization for the difference equation (10)

y(n)= -0.1y(n-1)+0.72y(n-2)+0.7x(n)-0.252x(n-2)
(10)

1
5.a)Consider the transfer function H(Z)= H1(Z).H2(Z) where (10)
H1(Z)= 1/1-a1z-1 and H2(Z)=1/1-a2Z-1 .
Find the output roundoff noise power. Assume a1=0.7 and a2=0.8 and find
output roundoff noise power in cascade form if b= 3(excluding sign bit)

b)Write short notes on Down sampling and Up sampling (5)

c) Determine expression for output y(n) as shown in figure (5)

x(n) 4 12 3
y(n)

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