dsp model exam question papers

1. GOJAN SCHOOL OF BUSINESS AND TECHNOLOGY
MODEL EXAMINATION OCTOBER - 2014
SUBJECT CODE/NAME : CS2403/DSP DATE : 27.10.2014
SEM/YEAR : VII/ IV CSE & V/III IT MAX MARKS : 100
STAFF NAME: R.RAMADHURAI AP/ECE DURATION: 3 HRS
PART- A (5X2 = 10)
1. What is meant by causal & non causal system?
2. Define time invariant system.
3. How many multiplications & addition are involved in radix-2 FFT?
4. What are the advantages of FFT algorithm over direct computation of DFT?
5. Distinguish between FIR filters and IIR filters.
6. What is Gibb’s phenomenon?
7. In the design of FIR digital filter, how is Kaiser Window different from other windows?
8. What are the desirable characteristics of the window function?
9. Define sampling rate conversion
10. How the image enhancement is achieved using DSP?
PART- B (5X16=80)
11.a. Check for following systems are linear, causal, time in variant, stable, static (16)
i) .y(n) =x(2n) (ii). y(n) = cos (x(n)) (iii). y(n) = x(n) cos (x(n) (iv) .y(n) =x(-n+2) (v). y(n) =x(n) +n x (n+1)
OR
b. (i) Find the inverse z- transform of 1/ (1-0.5 z-1) (1-z-1) (8)
(ii) Perform circular convolution of the two sequences X1(n) = {2,1,2,1} X2(n) = {1,2,3,4} (8)
12. a. (i) Discuss in detail the important properties of the DFT. (12)
ii) Find the 4-point DFT of the sequence x(n) = cos (nπ/4) (4)
OR
b. Derive the equation for Decimation - in time algorithm for FFT (16)
13. a. (i) Derive the equation for designing IIR filter using bilinear transformation. (10)
(ii) For the analog transfer function H(S) = 2/ (S+1)(S+2) . Determine H(Z) using impulse invariant technique. (6)
OR
b. Design a digital BUTTERWORTH filter that satisfies the following constraint using bilinear (16)
Transformation. Assume T = 1 sec.
0.9 ≤ | H(ω)| ≤ 1 ; 0 ≤ ω ≤ π /2
| H(ω)| ≤ 0.2 ; 3 π /4 ≤ ω ≤ π
14. a) Design a high pass filter hamming window by taking 9 samples of w(n) and with a cutoff frequency of 1.2
radians/sec (16)
OR
b. (i) Explain the characteristics of a Limit cycle oscillation w.r.t the system described by the difference equation
y(n) = 0.95y(n-1)+x(n).Determine the dead band of the filter. (12)
ii) Draw the product quantisation noise model of second order IIR filter.(4)
15. a. Write short notes on i) speech compression ii) sound processing (16)
OR
b. Explain speech vocoders and subband coding (16)

2. GOJAN SCHOOL OF BUSINESS AND TECHNOLOGY
MODEL EXAMINATION OCTOBER - 2014
SUBJECT CODE/NAME : CS2403/DSP DATE : 27.10.2014
SEM/YEAR : VII/ IV CSE & V/III IT MAX MARKS : 100
STAFF NAME: R.RAMADHURAI AP/ECE DURATION: 3 HRS
PART- A (5X2 = 10)
1. Define Sampling Theorem.
2. What is aliasing?
3. Distinguish between DIT and DIF -FFT algorithm.
4. Draw the basic butterfly diagram of radix -2 FFT.
5. What is Prewarping? Why is it needed?
6. What do you understand by backward difference?
7. What is the necessary and sufficient condition for linear phase characteristic in FIR filter?
8. What is meant by limit cycle oscillation in digital filter?
9. What are the two techniques of sampling rate conversion?
10. Give the applications of multirate digital signal processing.
PART- B (5X16=80)
11. a. (i) Find the periodicity of the signal x(n) =sin (2πn / 3)+ cos (π n / 2) (8)
(ii) Find the Z transform of (i) x(n) =[ (1/2)n – (1/4)n ] u(n) (8)
(ii) x(n) = n(-1)n u(n)
OR
b. (i) Determine the frequency response for the system given by
y(n)-y3/4y(n-1)+1/8 y(n-2) = x(n)- x(n-1) (8)
(ii) Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the step input. (8)
12. a. (i) Compute an 8-point DFT using DIF FFT radix -2 algorithm. x(n) = { 1,2,3,4,4,3,2,1} (10)
(ii) Calculate the DFT of the sequence X(n)={1,1,-2,-2} (6)
OR
b. (i) Find 4 point IDFT of the sequence x(n) =(0,1,2,3) (6)
(ii) Compute the DIT FFT for the sequence x(n) is (1,1,1,1,1,1,0,0) (10)
13.a.(i) Derive the equation for designing IIR filter using impulse invariant method. (10)
(ii) Find the digital transfer function H(Z) by using impulse invariant method for the analog
transfer function H(S)=1/(s+1)(S+2). Assume T=0.5sec (6)
OR
b. Design a digital Butterworth filter satisfying the following specifications
0.7 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.2, 0.6π ≤ ω ≤π with T= 1 sec .
Determine system function H(z) for a Butterworth filter using impulse invariant transformation. (16)
14. a. The desired frequency response of a low pass filter is given by
Hd(ω) ={ e -j3ω ; -3π/4 ≤ ω ≤ 3π/4
0; otherwise. Determine H(ejω) for M= 7using hamming window. (16)
OR
b. Obtain the i) Direct forms ii) cascade iii) parallel form realizations for the following system (16)
y (n) = 3/4(n-1) – 1/8 y(n-2) + x(n) +1/3 x(n-1)
15. a. (i) Explain decimation of sampling rate by an integer factor D and derive spectra for decimated signal (8)
(ii) Explain interpolation of sampling rate by an integer factor I and derive spectra for decimated signal(8)
OR
b. Explain about adaptive filters (16)