MU Computer Engineering (Semester 7)
Digital Signal Processing
May 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1(a) Fro the given causal sequences x(n) = {8, 9, 2, 3} and h(n) = {4, 3, 6} find the cross correlation.
5 M
1(b) State the condition for stability of LTI system and determine for the given discrete time system h(n) = (0.3)nu(n) + 5δ(n), is stable or not.
5 M
1(c) Differentiate IIR and FIR systems.
5 M
1(d) For the causal signal x(n) = {2, 2, 4, 4} compute four point DFT using DIT-Fft.
5 M

2(a) Check whether following system y(n) = 2x(n-1) + x(2n) is:
a. Linear or non Linear
2. Causal or non-causal
3. Time variant or Time invariant
4. Static or Dynamic
10 M
2(b) Draw the radix 2 DIT flow graph and find the DFT of the sequence x(n) = {10, 11, 8, 5} using FFT flow graph.
10 M

3(a) A For x(n)={2 3 →4 5 1 3}, plot the following Discrete Time Signals:
1) x(n-1)   2) x(n)u(-n)   3)x(n-1)u(n-1)   4) x(-n)u(n)   5) x(2n)
10 M
3(b) Determine whether or not the following signals are periodic.
If periodic specify its fundamental peroid,
1. x(n) = sin(0.25πn+0.4)
2. x(n) = cos(0.5nπ) + sin(0.25nπ)
10 M

4(a) For the FIR digital filter with impluse response given by
h(n) = 2δ (n-4) sketch the magnitude response of the filter.
10 M
4(b) State any five DFT properties.
10 M

5(a) Find circular convolution of x1(n) = {5, 6, 2, 1} and x2(n) = {3, 2, 1, 4} by computing DFT of x1(n) and x2(n).
10 M
5(b) Compute Linear Convolution of causal sequence x(n) = {7, 6, 4, 5, 2, 4, 5, 2, 3} and h(n) = {1 2 3 1} using fast overlap save method.
10 M

6(a) Write a detailed note on Carl's Correlation Coefficient Algorithm.
10 M
6(b) Write a detailed note on DSP Processor and Architecture.
10 M



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