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)

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 : -

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

\[H\left(e^{j\omega{}}\right)=0,\dfrac{3\pi{}}{4}\leq{}\left\vert{}\omega{}\right\vert{}\leq{}\pi{}\]

Use Hamming window of lenght = 7

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

\[H\left(e^{j\omega{}}\right)=0,\dfrac{3\pi{}}{4}\leq{}\left\vert{}\omega{}\right\vert{}\leq{}\pi{}\]

Use Hamming window of lenght = 7

10 M

3 (a)
If H

H

Given that sampling frequency Fs= 5000Hz Design FIR filter for length M=5 using Bartiett window

_{d}(ω)=1 for 0≤ f ≤ 800 Hz andH

_{d}(ω)=0 for f ≥ 800 HzGiven 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 :

\[0.9=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}1\\ \ \ \ \ \ \ \ \&0\leq{}\omega{}\leq{}\frac{\pi{}}{2} \\\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}0.2\ \ \ \ \ \\&\frac{3\pi{}}{4}\leq{}\omega{}\leq{}\pi{}\end{array}\right.\]

with sampling period T=1 sec, use Bilinear transformation method.

\[0.9=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}1\\ \ \ \ \ \ \ \ \&0\leq{}\omega{}\leq{}\frac{\pi{}}{2} \\\leq{}\left\vert{}H\left(e^{j\omega{}}\right)\right\vert{}\leq{}0.2\ \ \ \ \ \\&\frac{3\pi{}}{4}\leq{}\omega{}\leq{}\pi{}\end{array}\right.\]

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

(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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