Solve any

**four**:-
1 (a)
If F

(i) f = F/(2F

(ii) f = F

(iii) f = F/F

(iv) f = 2F/F

Justify the answer with an example.

_{s}is sampling frequency then the relation between analog frequency F and digital frequency f is :-(i) f = F/(2F

_{s})(ii) f = F

_{s}/f(iii) f = F/F

_{s}(iv) f = 2F/F

_{s}Justify the answer with an example.

5 M

1 (b)
The evaluation of correlation involves:-

(i) Shifting, rotation and summation.

(ii) Shifting, multiplication and summation.

(iii) Change of index, folding and summation.

(iv) Change of index, folding and shifting.

(i) Shifting, rotation and summation.

(ii) Shifting, multiplication and summation.

(iii) Change of index, folding and summation.

(iv) Change of index, folding and shifting.

5 M

1 (c)
Compare IIR and FIR.

5 M

1 (d)
State and explain Parseval's Theorem in DFT.

5 M

1 (e)
State the relationship between Z-transform and DTFT.

5 M

2 (a)
Determine the energy of the sequence:-

x[n] = (0.5)

=3

and plot the same.

x[n] = (0.5)

^{n}n≥0=3

^{n}n<0and plot the same.

10 M

2 (b)
If x[n]={

h[n] = 1 for 0≤n≤5

=0 elsewhere

Determine linear convolution.

**1**,-2,1} andh[n] = 1 for 0≤n≤5

=0 elsewhere

Determine linear convolution.

10 M

3 (a)
Determine the response of the system:-

y[n] = (5/6)y[n-1] - (1/6)y[n-2] + x[n]

For inputx[n] = δ[n] - (1/3)δ[n-1]

y[n] = (5/6)y[n-1] - (1/6)y[n-2] + x[n]

For inputx[n] = δ[n] - (1/3)δ[n-1]

10 M

3 (b)
Using Z transform properties prove that:-

\[n x[n]\overset{z}\leftrightarrow {-z} \dfrac{dx(z)}{dz}\\ if \ x[n]\overset{z}\rightarrow x(z) \]

\[n x[n]\overset{z}\leftrightarrow {-z} \dfrac{dx(z)}{dz}\\ if \ x[n]\overset{z}\rightarrow x(z) \]

10 M

4 (a)
The system function of the LTI system is given as:-

Specify ROC of H(z) and determine unit sample response h(n) for the following conditions:

(i) Stable system.

(ii) Causal system.

Specify ROC of H(z) and determine unit sample response h(n) for the following conditions:

(i) Stable system.

(ii) Causal system.

10 M

4 (b)
Explain Overlap add and Overlap save method.

10 M

5 (a)
Find DFT of the following sequence using FFT:-

x(n) = {1,1,1,0,0,0,1,1}

x(n) = {1,1,1,0,0,0,1,1}

10 M

5 (b)
Using the result derived in Q.5 (A) Find the DFT of the signal and not otherwise:-

x

x

x

_{1}[n] = {1,0,0,0,1,1,1,1}x

_{1}[n] = {1,1,1,1,1,0,0,0}
10 M

6 (a)
Determine the frequency, magnitude and phase response of the system given by the differential equation:-

y[n] = x[n] - x[n-1] + x[n-2]

y[n] = x[n] - x[n-1] + x[n-2]

10 M

6 (b)
Find the 4pt. DFT of the sequence:-

x[n] = cos(0.25nπ)

x[n] = cos(0.25nπ)

10 M

Write short notes on any

**four**:-
7 (a)
Geortzel Algorithm.

5 M

7 (b)
Give difference between DSP and Microprocessor.

5 M

7 (c)
Applications of DSP [any two].

5 M

7 (d)
Mapping of s-plane to z-plane.

5 M

7 (e)
Properties of DTFT.

5 M

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