MU Digital Signal Processing & Processors - May 2012 Exam Question Paper

MU Electronics Engineering (Semester 6)
Digital Signal Processing & Processors
May 2012

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) Show that FIR filters are linear phase filters. Define group delay and phase delay.

8 M

1 (b) find the response of the system given by difference equation y(n)-5y(n-1)+6y(n-2) = x(n) for (i) x(n) = ?(n) and (ii) x(n) = U(n)

6 M

1 (c) Draw direct form - I and Direct form-II realization of the system given by
y(n)-3/4?y(n?1) + 1/8?y(n-2) = x(n) + 1/3?x(n-1)

6 M

2 (a) Derive Radix-2 Decimation in Time Fast Fourier Transform and draw its signal flow graph

10 M

2 (b) Design FIR digital filter by using window method for the following specification : -

H (e^{j ω}) = e^{- j 3 ω} - \frac{3 π}{4} \leq ω \leq \frac{3 π}{4}

$H\left(e^{j\omega{}}\right)=e^{-j3\omega{}}\ \ \ \ -\frac{3\pi{}}{4}\leq{}\omega{}\leq{}\frac{3\pi{}}{4}$

H (e^{j ω}) = 0, \frac{3 π}{4} \leq | ω | \leq π

$H\left(e^{j\omega{}}\right)=0,\dfrac{3\pi{}}{4}\leq{}\left\vert{}\omega{}\right\vert{}\leq{}\pi{}$
Use Hamming window of lenght = 7

10 M

3 (a) If H_d(ω)=1 for 0≤ f ≤ 800 Hz and
H_d (ω)=0 for f ≥ 800 Hz
Given that sampling frequency Fs= 5000Hz Design FIR filter for length M=5 using Bartiett window

10 M

3 (b) Find 8-point FFT of x(n)= { 1,2,2,2,1 } using signal flow graph of Radix- 2 Decimation in frequency FFT

10 M

4 (a) Design a digital Butterworth filter satisfying the following constraints :

0.9 = {\begin{cases} \leq | H (e^{j ω}) | \leq 1 \\ & 0 \leq ω \leq \frac{π}{2} \\ \leq | H (e^{j ω}) | \leq 0.2 \\ \frac{3 π}{4} \leq ω \leq π \end{cases}

$0.9=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}1\\ \ \ \ \ \ \ \ \&0\leq{}\omega{}\leq{}\frac{\pi{}}{2} \\\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}0.2\ \ \ \ \ \\&\frac{3\pi{}}{4}\leq{}\omega{}\leq{}\pi{}\end{array}\right.$
with sampling period T=1 sec, use Bilinear transformation method.

12 M

4 (b) State and derive Geortzel algorithm, also state its application

8 M

5 (a) For the analog tansfer function \[H\left(s\right)=\frac{3}{\left(s+2\right)\left(s+3\right)}\\] Determine H(z) with sampling period T=0.1 sec using
(i) Impulse Invariant method
(ii) Bilinear Transformation method

10 M

5 (b) Describe the application Geortzel algorithm in dual tone multi- frequency detection.

10 M

6 (a) With a suitable block diagram describe sub-band coding of speech signals.

10 M

6 (b) With a neat diagram describe frequency sampling realization of FIR filters.

10 M

7 (a) Explain up sampling by non-integer factor, with a neat diagram and waveforms

10 M

7 (b) Explain the application of DTSP in adaptive echo cancellation.

5 M

7 (c) Describe the concept of digital resonator

5 M

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