MU Instrumentation Engineering (Semester 6)
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


Answer the following (Any four)
1(a) \( H(z)=\dfrac{5z^2-12z}{z^2-6z+8} \) show that h(n) = 2n+4n+1 and find first 5 vaccies.
5 M
1(b) What are the advantage of DSP & define sampling theorem.
5 M
1(c) Determine IDFT of c(k) = {3, 2+j, 1, 2-j} by using DIF Fft algorithm.
5 M
1(d) Convert the along filter with system function \( H(s)=\dfrac{s+0.1}{(s+0.1)^2+16} \) into a digital IIR filter using Bilinear transformation. The resanant frequency of ωr = π/2.
10 M
1(e) Write a short note on Decimation by a integar factor.
10 M

2(a) If x(n) = {2, 3, 4, 5} find (i) DFT of x(k) (ii) using result obtained in one not otherwise find the DFT of following sequences.
x1(n) = {5, 3, 4, 5}, x2(n) = {3, 4, 5, 2} [ 4, 5, 2, 3 ] x3 = [ 2, 5, 4, 3 ]
10 M
2(b) Perform Linear concolution using DIT FFT algorithm.
x(n) = {1, 2, 3}       h(n) = [1, 2]
10 M

3(a) Determine the output of a Lirear FIR & whose impuse response
h(n) = {2, 2, 1}
x(n) = {3, 0, -2, 0, 2, 1, 0, -2, -1, 0} using over lap save method.
10 M
3(b) Derive & draw the FFT for n=6=2×3 using DIT FFT algorithm.
10 M

4(a) Determine the frequency response plot magnitude & phase response for the frequency ω = 0, π/4, π/2, 3π/4, & π.
y(n) = x(n) + 0.9 x(n-2) - 0.4 y (n-2)
10 M
4(b) Realize the system by using, direct form - I cascade & parallel Realization.
y(n) = -0.1y(n-1) + 0.2y(n-2) + 3x(n) + 3.6 × (n-1) + 0.6 × (n-2)
10 M

5(a) Design IIR butter worth filter to satisfy following condition.
0.8 < | H (e) | ≤ 1         for 0 ≤ ω ≤ 0.2
          | H (e) | ≤ 0.2       for 0.6π ≤ ω ≤ π
using Bilirear transformation method Assume T = 1 sec.
10 M
5(b) A Linear phase FIR filter has derived
Ha(e) = 0         for -π/4 ≤ ω ≤ π/4
            = e-j2ω     for π/4 |≤| W| < π
Design the filter using Hanning window Assume m=5 and also draw linear phase Realization.
10 M

6(a) Explain the Architecture of Tex as -320 Dsp processor.
10 M
6(b) Write a short note on Interpalation.
5 M
6(c) Difference between IIR & FIR filter.
5 M



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