1 (a)
Classify the following system on the basis of linearity and time variance/invariance:

(i) y[n] = 4x[n] - 2y[n-1]

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

(iii) y[n] + 2 y

(iv) y[n] - 2 y[n-1] = 2

(v) y[n] = x[-n]

(i) y[n] = 4x[n] - 2y[n-1]

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

(iii) y[n] + 2 y

^{2}[n] = 2x[n] - x[n-1](iv) y[n] - 2 y[n-1] = 2

^{x[n]}x[n](v) y[n] = x[-n]

5 M

1 (b)
Find the number of complex addition and complex multiplication required to find DFT for 16 point signal. Compare them with number of computations required, if FFT algorithm is used.

5 M

1 (c)
Prove that discrete time harmonics are not always periodic in frequency.

5 M

1 (d)
Compare IIR and FIR.

5 M

2 (a)
Determine causal, non-causal and both sided signal associated with z-transform.

x(z) = [1 + 1.5z

x(z) = [1 + 1.5z

^{-1}+ 0.5z^{-2}]^{-1}
10 M

2 (b)
If x[n] = [3,2,1,2] and h[n] = {1,

**2**,1,2}, then determine linear convolution.
10 M

3 (a)
Consider a sequence x[n] = {1,2,1,2,0,2,1,2}. Determine DFT using DITFFT.

10 M

3 (b)
Find DFT of the sequence x[n] = {1,2,3,4} and using this result and not otherwise, find DFT of

(i) x

(ii) x

(iii) x

(i) x

_{1}[n] = {1,0,2,0,3,0,4,0}(ii) x

_{2}[n] = {1,2,3,4,0,0,0,0}(iii) x

_{3}[n] = {1,2,3,4,1,2,3,4}.
10 M

4 (a)
The transfer function of discrete time system has poles at z=(1/3),z=(+-j/2) and z=-2(+-)j and zeros at z=0 and z=-1.

(i) Sketch pole-zero diagram.

(ii) Derive the system transfer function.

(iii) Develop difference equation.

(iv) Find if the system is stable.

(i) Sketch pole-zero diagram.

(ii) Derive the system transfer function.

(iii) Develop difference equation.

(iv) Find if the system is stable.

10 M

4 (b)
Derive the composite radix for δ=2.3 algorithm. Draw the flow chart.

10 M

5 (a)
Explain Overlap add and Overlap save method.

10 M

5 (b)
Determine the steady state response of the system

H(z) = (3z

x[n]=(0.6)

H(z) = (3z

^{2})/(z^{2}-z + 1)for the inputx[n]=(0.6)

^{n}+ 2(0.4)^{n}cos(0.5nπ - 100^{0}).
10 M

6 (a)
Show DF-I, DF-II, cascade and parallel realization for

10 M

6 (b)
Let

let the input x[n] = 4 u(n) and the initial conditions be

y[-1]= 0, y[-2] = 12. Find:-

(i) Zero input response.

(ii) Zero state response.

(iii) Total response.

let the input x[n] = 4 u(n) and the initial conditions be

y[-1]= 0, y[-2] = 12. Find:-

(i) Zero input response.

(ii) Zero state response.

(iii) Total response.

10 M

Write short notes on any

**four**:-
7 (a)
Properties of DTFT.

5 M

7 (b)
Goertzel Algorithm.

5 M

7 (c)
Mapping between s-plane and z-plane.

5 M

7 (d)
Applications of DSP to Biomedical field.

5 M

7 (e)
TMS 320C5X series processor.

5 M

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