University of Mumbai 2004 B.E Computer Science SEM-7 digital signal processing - Question Paper

digital signal processing (dec. 2004)
N.B.:
ques. No. one is compulsory.
Any 4 ques. out of remaining ques..
Assumptions made should be clearly said.
Figures to the right indicate marks.
1. State whether every of the subsequent statement is actual or false. Justify
your ans in four or five phrases. (20)
Linear phase filters are always IIR
For a causal system I h(n) I tends to zero, as n tends to infinity, the system is stable
A stable filter is always causal
A stable, causal FIR filter has its poles lying anywhere inside the unit circle in the z-plane
IIR filters have recursive realization always.
2. (a) x (n )= d (n) + d(n-1)- d(n-2) + d(n-3) + d(n-4) + dn-5) (10)
h(n)= -d(n) + 2d(n-l)-d(n-2). obtain y(n) using linear convolution,
(b) find the plot of magnitude and phase response of a filter with the
subsequent impulse response h(n) = { -1,2, -2,1}
Comment of the kind of filter based on band magnitude and phase
response. (10)
3. (a) Causal system has the subsequent transfer function (20)
H(z) = Z2 / ( Z2 – 0.1Z - 0.12)
ROC | Z| > 0.4

Plot the pole-zero locations in the z-plane.
Findh(n)by i) partial fraction expansion, ii) power series expansion by long division method.
obtain the difference formula and obtain h(n) from the difference formula.
Show the direct form realization and canonic realization. Is there a difference in the 2 realizations.
4. The impulse response of a system is provided by (20)
h(n) = (l/2)nu(n) + (-l/5)nu(n)
obtain H(z) along with ROC.
obtain Hfe**) directly and from z-transform.
Comment on the system as causal, FIR, and BIBO stable.
obtain the energy in the sequence h(n).
provide a parallel realization of the system.
5. (a) If x(n) = dn)+d(n-l) + d(n-2), (10)
FindX(ejw)
obtain X(k) 4-point DFT (do not use FFT)
Show that DFT is the sampled version of |X(ejw) |.
(b) A sequence x(n) = {a, b, c, d} has DFTX(K) = {1, 2, 3,2}. obtain x(n)
using four point DIF-FFT. If y(n) = { a, d, c, b } what is Y(K). Use DFT
properties and state the property used. (10)


6. (a) An ideal lowpass filter has the response (10)
H (ejw) = two ejw? |W| < WC
= 0 WC < |W| obtain h(n)? For a transition width < ?/32, compute the window length and the values of a for (i) rectangular window (ii) hamming window.
(b) Design and realize a low pass filter using the bilinear transformation method to satisfy the subsequent characteristics
i) monotonic stop band and pass band,
(ii) -3dB cut off frequency of0.57irad,
(iii) stop band attenuation of 15dB at 0.77trad. (10)

7. (a) Write notes on the applications of DSP in (12)
(a) Image processing (b) Speech Processing & (c) Telecommunication
(b) discuss a DSP processor. State advantages of DSP processor over
microprocessor for DSP applications. (8)

Earning:   Approval pending.