7/29/2019 DSP Model Question

1/4

Digital Signal Processing (EC-602)Electronics & Communication Engineering

Model Question2013

Full Marks 70 Time 3 Hours

Group- AChoose the correct alternative for any ten of the following. 101=10

1. (i) Infinite memory system is also known as

(a) FIR system. (b) IIR System. (c) Digital system. (d) Analog system.(ii) Rectangular window used for designing FIR filters, the peak amplitude of side lobe is

(a) -40dB (b) -3dB. (c) 0dB. (d) -13dB.

(iii) Zero padding a signal

(a) Reduce aliasing. (b) Increase time resolution. (c) Has no effect. (d) Increasefrequency resolution.

(iv) if X(k) represents the 8-point DFT of x(n)={1,1,1,1,1,0,0,0}, X(0) is

(a) 3 (b) 6 (c) 0 (d) 1

(v) A discrete-time LTI systems described by the following input-output equations arecausal or non-causal.

(a) h(n)=0, n0. (c) h(n) is positive, n| |

B. - n u(-n-1) 2. , ROC: |z|>| |

C. -n n u(-n-1) 3. , ROC: |z|

7/29/2019 DSP Model Question

2/4

(ix) If x(n) X(z), then the valid one is,

(a) x(-n) X(z) (b) x(-n) z X(z) (c) x(-n) (X(z)/z) (d) x(-n) X(1/z)

(x) x(n) is an energy signal when

(xi) If the Fourier transform of x(n) is X( ), then the Fourier Transform of nx(n) is

(xii) If f(t) F(j ) then Fourier Transform of exp(j 0t)f(t-t0) is(a) F(j )exp(-j t 0) (b) F(j -j 0) (c) F(j -j 0)exp(-j t 0) (d) none of

these.Group B

Answer any three of the following questions.35=15

2. When a system is said to be stable? Find whether the system with impulse response

3. State the properties of convergence for the Z-transform.4. Proof the digital system is stable for |z|

7/29/2019 DSP Model Question

3/4

(c) Compute an 8-point DFT of the following sequences using DIT algorithm.

5+3+7=15

x(n)= {1,-1,1,-1,0,0,0,0}9. (a) Determine the IDFT of X(k)={2,(3+j),4,(3-j)}.

(b) Why FFT is needed? What are differences and similarities between DIF and

DIT algorithms?(c) What is rectangular window?

(d) How a rectangular window used to design FIR filter?

5+(2+2)+2+4=15

10. (a) Determine H(z) for a Butterworth filter satisfying the following constraints

With T=1sec, apply impulse invariant transformation.(b) Distinguish between FIR and IIR filter.

(c) What is warping effect? How can you remove this effect?7+2+2+2+2=15(d) What is window and why it is necessary?(e) What are the advantages of cascade realization and direct-form realization?

11. (a) A low pass filter is to be designed with the following desired frequencyresponse

Hd(ej) = e- j2 , -/4 /4

= 0, /4 Determine the filter coefficients hd(n) if the window function is defined as

w(n) = 1, 0 4= 0, otherwise

(b) The length of an FIR filter is 13. If the filter has a linear phase, show that

8+3+ (2+2) =15

(c) Obtained the direct form II and cascade realization for the systemy(n)= - 0.1y(n-1) + 0.2y(n-2) + 3x(n) + 3.6x(n-1) + 0.6x(n-2)

12. Write the short note (any three).35=15

(a) Final value theorem regarding Z-transform.(b) Bilinear Transformation.

(c) Overlap-save method.(d) Group delay and phase delay.(e) Chebyshev Filter.

7/29/2019 DSP Model Question

4/4