1 (a)
Find the Z-transform and hence DFT of:-

x(n) = (0.25)

x(n) = (0.25)

^{n}u(n+4)
5 M

1 (b)
Find the magnitude and phase response of the system described by the difference equation:-

y(n) = x(n) + [(1/3) x(n-1)] + [(1/6) x(n-2)]

y(n) = x(n) + [(1/3) x(n-1)] + [(1/6) x(n-2)]

5 M

1 (c)
Derive Parseval's Energy Theorem. Also state the significance of the same.

5 M

1 (d)
Calculate the speed improvement factor in calculating 256 point DFT of sequence using direct computation and using FFT algorithm.

5 M

2 (a)
Find Energy and power of the following signals:-

(i) x(n) = (1/3)

(ii) x(n) = 3 cos(4πn + θ)

(i) x(n) = (1/3)

^{n}for n≥0 = 3^{n}for n<0(ii) x(n) = 3 cos(4πn + θ)

8 M

2 (b)
Test the following systems for linearity and time invariance:-

(i) y(n) = a

(ii) y(n) = 2x(n) + 1/[x(n-1)]

(i) y(n) = a

^{x(n)}(ii) y(n) = 2x(n) + 1/[x(n-1)]

6 M

2 (c)
Determine the transfer function, impulse response and step response for the system given by:-

y(n) = y(n-1) + x(n) + x(n-1)

y(n) = y(n-1) + x(n) + x(n-1)

6 M

3 (a)
Determine the inverse ZT for

X(z) = z/[(3z

ROC |z|>1

X(z) = z/[(3z

^{2}- 4z + 1)ROC |z|>1

8 M

3 (b)
Obtain Cascade and Parallel realization of the second order DT linear system defined by:-

y(n) - 0.75 y(n-1)+ 0.125 y(n-2) = x(n) + 0.3 x(n-1)

y(n) - 0.75 y(n-1)+ 0.125 y(n-2) = x(n) + 0.3 x(n-1)

12 M

4 (a)
Determine the circular convolution of the two sequences x

x

x

_{1}(n) and x_{2}(n) if-x

_{1}(n) = δ(n) + δ(n-1) - δ(n-2) - δ(n-3) andx

_{2}(n) = δ(n) - δ(n-2) + δ(n-4)
10 M

4 (b)
For the pole-zero plot of a system shown below:-

(i) Find the equation of magnitude response.

(ii) Plot the magnitude response.

(iii) Identify the type of system based on pass band.

(i) Find the equation of magnitude response.

(ii) Plot the magnitude response.

(iii) Identify the type of system based on pass band.

10 M

5 (a)
Given x(n)=2

^{n}and N=8, find X(k) using DITFFT algorithm.
10 M

5 (b)
For x(n) = {1+5j, 2+6j, 3+7j, 4+8j}, find DFT X(k). Using the result above and not otherwise, find DFT of the following sequences:-

x

x

x

_{1}(n) = {1,2,3,4} andx

_{2}(n) = {5,6,7,8}
10 M

6 (a)
Explain the overlap-add and overlap-save method for filtering of long data sequences.

10 M

6 (b)
Draw the functional block diagram of TMS320C5X processor and explain various functional units.

10 M

7 (a)
Using DFT/IDFT, find circular convolution of

x

x

_{1}(n) = {1,1,2,2} and x_{2}(n) = {1,2,3,4}
10 M

7 (b)
Classify the following systems as FIR/IIR, Min/Max/Mixed Phase and specify the passband from the pole-zero plot shown below:-

10 M

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