University of Mumbai 2007-6th Sem B.E Electrical and Electronics Engineering Signal Processing-II - exam paper
( 3 Hours)
N.B. (1) Question No. 1 is compulsory.
(2) Attempt any five questions including question No. 1.
(3) Figures to the right indicate full marks.
(4) Assume any suitable data whenever required but Justify the same.- ,A\
1. (a) A second order all-pass filter has a zero at 0*5 Z.160. Find the location of other poles 5
pass filter has a zero at u*b L ieuw. nna tne location ot omer poles and zeros and sketch the pole-zero plot in the z-plane. Also, find the system transfer function.
(b) Show thal the zeros of a linear phase FIR filter occur at reciprocal locations. Also, show that FIR filter with anti-symmetric impulse response and odd length will have compulsory zeros at 2 = 1.
(c) Compute the DFT of the sequence x(n) = cos ( n n/2), where N = 4, without using any FFT algorithm.
(d) Show the mapping from s-plano to z-plane using impulse invariance method and explain its limitation.
2. (a) Identify ths following systems based on their pass-bands, FIR/UR, minimum/maximum phase, 12 linear/ncn-linear phase, stable/unstable system etc. Explain your answer with appropriate reason.
He f rj
 |
> le(t) |
 |
ZrCzJ |
(b) DT-LTI system is characterized by the transfer function
2(32-4)
H(z) =
3)
Specify the ROC of H(z) and determine h(n) for
(I) The eyetem is stable (ii) The system is causal (iii) The system is anticausaJ.
Con. 4850-CD-5517-07. ____ 2 P IK* t
3. (a) For fhe aitier&nce equation given below*: rHflT~
y(n) + b2 y (n - z) =0 for n 0. 2 r
where initial conditions are y( - 1) = 0 and y( - z) = - 1.
( nit
Prove thal y(n) = bn + 2 cos I ~~~
(b) Sketch the magnitude and phase response of a system with impulse response ; h(n) * ( 1, 2, 2, 1 } over the frequency range - 3n to 3n.
4. (a) A digital low-pass filter is required to meet the following specifications :
Pass band ripple : 1 dB
Pass band edge : 4 kHz
Stop band attenuation : > 40 dB
Stop band edge : 6 kHz
Sampling rate : 24 kHz Find the order of Butterworth and Chebyshev filter using bilinear transformation.
(b) A low-pass filter has the response
Hd (e|w) = 2 -e'|w for < w s -
2 2
= 0 otherwise
71
Find h (n) for transition width <
Calculate the window length and the value of 'a' for
(i) Rectangular window, (ii) Hamming window.
5. (a) Using inverse FFT tlow-graph find the sequence x(n) whose OFT is given by :
X(k) (2.- 1. A, 6, 2, 6,-4,1 }
(b) Let x, (n) = { 1, 2, 3, 4 ) and x2 (n) { 5, 6, 7, 8 }. Find XT(k) and X2(k) of the above sequence by performing DFT computation only once.
6. (a) Consider the causal linear shift-invariant filter with system function
1 f-0-875z-'
H(z)
(1 + 0-2z-1 + 0 9z 2 ) (1 -0-7z-1)
Draw a signal flowgraph for this system using :
(i) Direct form I
(ii) Direct form II
(iii) A cascade of first and second-order systems realized in direct form II.
(iv) A parallel connection of first and second-order systems realized in direct form II,
(b) Compute the 8*point circular convolution for the following sequences :
x, (n) = { 1, 1. 1, 1, 0, 0,0,0)
x2(n) = sin > 0 < n < 7.
7. Write notes on the following
(a) Radix-2 FFT algorithms
(b) DSP processors
(c) Digital oscillator
(d) Window functions and designing of FIR filters.
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| Earning: Approval pending. |
