Set No:

1

Code No: NR/RR-311102 III B.Tech. I Semester Regular Examinations, November-2004 DIGITAL SIGNAL PROCESSING (Common to Bio-Medical Engineering and Electronics and Computer Engineering) Time: 3 Hours Max. Marks: 80 Answer any FIVE Questions All questions carry equal marks --1.a) What is meant by Digital signal Processing? What are the applications of DSP? b) Check whether the given system is i) Linear ii) Time invariant iii) Causal iv) Stable v) Static or not: y(n) = Sgn[x(n)]. State and prove linearity and circular shift properties of DFT. i) show that iF x(n) =-x(n-1-n) then its DFT X(k) at K=0, X(0)=0. ii) It N is even and iF x(n) =x(N-1-n) then ITS DFT X(k) at K=N/2, X(n/2)=0.

in

2.a) b)

-j

Prove symmetry and periodicity properties of the twiddle factor WN  e Develop a 16-point radix-2 DIT FFT algorithm.

4.a)

Find the general solution of the first order difference equation. y ( n)  0.9 y ( n  1)  0.5 x( n)  0.9 x( n  1) for n  0 with y ( n  1)  5.

b)

Find whether the given system in stable or not using Jury’s test: 3 1 1 y(n) = y ( n  1)  y ( n  2)  x (n)  x( n  1) 4 8 3 What are the basic building blocks of realization structures? And what are the advantages of representing digital systems in the block diagram form? Explain the characteristics of Butter worth filter. Design a digital filter to meet the following specifications. Using bilinear method: Sampling frequency : 8KHZ. Pass Band : 0-13KHZ. Maximum ripple in pass band : 1dB. Stop : beyond 2.6KHZ. Minimum attenuation in stop band : 25dB.

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6.a) b)

or

5.a)

Z2 and x(n) = 4. u(n). and the initial conditions be 1 1 2 Z  Z 6 6 y ( 1)  0, y (2)  12. Find zero-input and zero-state response of the system H(Z).

Let H ( Z ) 

uW

b)

.

ld .

3.a) b)

2 N

What are the advantages and disadvantages of FIR and ITR filters. Design an FIR LPF with fe = 1KHZ and sampling rate of 4KHZ with 11 samples using fourier series method.

Aj

7.a) b)

8.a)

b)

Explain in detail how analysis of continuous time signals can be made using DFT. What is a vocoder? Explain with a block diagram.

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Set No:

2

Code No:NR/RR-311102 III B.Tech. I Semester Regular Examinations, November-2004 DIGITAL SIGNAL PROCESSING (Common to Bio-Medical Engineering and Electronics and Computer Engineering) Time: 3 Hours Max. Marks: 80 Answer any FIVE Questions All questions carry equal marks --1.a) What are the advantages and limitations of DSP over analog signal processing? b) Check whether the given system is i) Linear ii) time invariant iii) Causal n 1

iv) Stable v) Static or not

y ( n) 

 x(k ) .

2.a) b)

in

K  

It x1(n)=(n+1), 0 n 5; and x2(n)=(n-2), 0  n  2 sketch their 6-point circular convolution State and prove duality and circular convolution properties of DFT. Develop an 8-point DIT FFT algorithm. Find the DFT of given sequence using DIF FFT algorithm: x(n) = {1, -1, 1, -1, 1, -1, 1, -1}.

4.a)

Find the value of x(0) for the sequence that has a z-transform. Z  3  Z 1 1 X (Z )  , Z  . And verify the initial value theorem. 3  1 1  1 2  1  Z 1  Z   4  3  Consider the following difference equation: y (n)  y n  2   x(n)  x(n  1) If x(n) =10u(n) and y(-2) = -10 and y(-1)=0, find the o/p sequence y(n) for n  0.

b)

Determine frequency, magnitude and phase responses and time delay of the 1 system y (n)  y (n  1)  x(n)  x(n  1) . 4 Draw the direct form-I & Direct form-II realizations of the given system: Z 1  3Z 2 H (Z )  . (10  Z 1 )(1  0.5Z 1  0.5Z 2 ) Explain about prototype Chebyshev filter Design a digital filter to meet the following specifications:  1dB Pass band ripple : Pass band edge : 4KHZ. Stop band attenuation :  40dB. Stop band edge : 6KHZ. Sample rate : 24KHZ. Use bilinear transformation method.

Aj

nt

6.

or

5.a)

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b)

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3.a) b)

7.a) b)

What are the characteristics of linear phase filters? Explain. Design a HPF using Hamming window, with a cutoff-frequency of WC =1.2 rad/sec and N = 9 and realize the filter.

8.a)

Explain linear filtering using DFT? What are the advantages of this method than time-domain approach? Explain. Explain about the digital model of speech production. @@@@@

b)

Set No:

3

Code No:NR/RR-311102 III B.Tech. I Semester Regular Examinations, November-2004 DIGITAL SIGNAL PROCESSING (Common to Bio-Medical Engineering and Electronics and Computer Engineering) Time: 3 Hours Max. Marks: 80 Answer any FIVE Questions All questions carry equal marks --1.a) State and prove the condition for the stability of an LTI discrete time systems. b)

Determine the step response of an LTI system given by h (n )  (0.5)  n u (n ), for all n It x1(n) = (N-n), 0  n  N-1, N = 6 and x2 (n) = (n) + (n-1), 0  n  4. Sketch their N-point circular convolution for N=6 and for N=10.

3.a) b)

Develop an 8-point DIF FFT algorithm. Find the DFT of given sequence using DIT FFT algorithm: x(n) = {1, -j, 1, -j, 1, -j, 1, -j}

4.a)

The

ld .

sequence y(n) in the solution to the LCCDE 3 1 y (n)  y (n  1)  y (n  2)  x(n), n  0. with x (n)   (n). Find a set of 2 2 initial conditions on y(n) for n<0 so that y(n)=1 for n  0. Use the residence theorem to find the value of x(n) at n = 10 when 1  3Z  4 X (Z )  , Z  0. 6 1  0.2 Z 1 1  0.6 Z 1



b) 6.a) b)



Obtain the cascade and parallel realization structures of the given signal: 3 1 1 y (n)  y (n  1)  y (n  2)  x(n)  x(n  1) . 4 8 3 Compare direct form –I & direct form –II realizations of ITR and FIR systems

uW

5.a)



or

b)

in

2.a) b)

Derive an expression for bilinear transformation method. Use the bilinear transformation to design a discrete time Chebyshev high pass filter with an equiripple pass band with

 

 

0  H e jw  0.1, 0  w  0.1 and 0.9  H e jw  1.0, 0.3  w  . Explain the windowing technique in the design of FIR filter. Design a HPF using Hamming window, with a cutoff frequency of 2 rad/sec. and N = 9. and realize the filters.

8.a)

What are various speech processing problems? Explain the model of speech waveform. What is STFT? How it is used for analysis & synthesis of speech signals?

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7.a) b)

Aj

b)

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Set No:

4

Code No: NR/RR-311102 III B.Tech. I Semester Regular Examinations, November-2004 DIGITAL SIGNAL PROCESSING (Common to Bio-Medical Engineering and Electronics and Computer Engineering) Time: 3 Hours Max. Marks: 80 Answer any FIVE Questions All questions carry equal marks --1.a) Explain about Gibb’s phenomena with an example. b) Find the convolution of the two finite-length sequences: x(n)  0.5n[u (n)  u (n  6)]

in

 n  h(n)  2 sin   u (n  3)  u (n  4).  2 

State and prove Parseval’s relation for the DFT. It x1(n)= (n) +(n-1)+(n-2); x2(n)= 2(n) -(n-1)+2(n-2); compute x1(n) (3) x2(n).

3.a)

Prove that the computation of DFT using FFT method is efficient than direct computation of DFT. Compute inverse DFT of given sequence using DIT FFT method: X(K) = {8, 0, 0, 0, 0, 0, 0, 0}. Z 2  3Z Find the inverse of X ( Z )  Z  2  Z 2  2 Z  2

b) 4.a)



n



ld .

2.a) b)

Given h(n)   (n)  0.40.5 .u (n), obtain the difference equation and from that verify the given system is FIR or ITR.

5.a)

Realize the system in cascade and parallel forms: 1 1  Z 1 2 H (Z )  . 1  1  2  1 1  2  1  Z  Z 1  Z  Z  4 2    Check the above system for its stability using Jury’s test. And verify the same by plotting its Pole-Zero diagram. Compare and contrast Butter worth and Chebyshev filters. The specification of the desired low pass digital filters is 0.9  H w  1.0, 0  w  0.25

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6.a) b)

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b)

or

b)

H w  0.24, 0.5  w   Design a Chebyshev digital filter using impulse invariant transformation.

Explain Fourier series method of designing digital filters. Design a BPF to pass frequencies in the range 2 to 4 rad/sec using Hamming window with N=7. and realize the filter.

Aj

7.a) b)

8.a) b)

Write notes on speech synthesis. What is an ambiguity function? What is its role in the design of radar signals using matched filtering? Explain briefly. @@@@@