St
B.E./B.Tech.
St. Xaviers Catholic College of Engineering, Chunkankadai,
Nagercoil 629 003.
Seventh Semester
Computer Science Engineering
CS2403 Digital Signal Processing
Model Examinations October-2014Time: 3 Hours
Maximum: 100 marks
ANSWER ALL QUESTIONS
PART A (10 x 02 = 20 marks)
1. State and prove Convolution property of Z-transform?
2. Draw Radix -2 butterfly Structure for DIT- FFT Algorithm?
3. Find DFT for { 1,0,0,1}4. State Sampling theorem, and find
Nyquist rate of the signal x(t)= 5 sin 250t + 6 cos 300t
5. What is Gibbs phenomenon?
6. Define finite word length effects. List errors due to finite
word length in filter design.
7. Give the Properties of stability.
8. Give short notes on DCT.9. How overflow limit cycles can be
eliminated?10. Give the properties of discrete time sinusoids.PART
B (05 x 16 = 80 marks)
11. a. Find the Z-Transform of
(iii) x(n)= -bn u(-n-1)
(4) (iv) x(t)=[sin t] u(t)
(6)OR11.b. Check whether the system is causal,Linear Time
invariant, stable or not.
(16)
i. y(n)= x(n)(cos n) ii. y(n)= x(n) - x(n-1)
iii. y(n)= x(n)+3x(n+4)
iv. y(n)=exp{x(n)}
12.a. A filter is to be designed with the following desired
frequency response
(16)
Hd(ej )={0
, | | /4
e-j3 , /4< || }
Determine the filter coefficients h(n) using the hanning window.
Find the frequency response
of the filter. Realise the structure also.
OR
12.b. i)Derive the equation for DIF FFT algorithm
(10)
ii) Find the inverse Z-Transform of 1/ [(1-.5 z-1) (1-.25
z-1)]
(6)
13.a. Find the convolution and correlation for x (n) = {0, 1,-2,
3,-4} and (16) h (n)={0.5,1,2,1,0.5} OR
13.b. An 8-point sequence is given by x(n)={2,2,2,2,1,1,1,1}
compute 8 point DFT of x(n) by(i) Radix-2 DIT-FFT
(8)(ii) Radix-2 DIF-FFT
(8)
14.a. i) Find the response of an LTI system with impulse
response h (n)={-4,-4,-6} for
input x(n)={1,2,3,4,5} using circular convolution
(8)
ii) Give the steps involved in designing the filter using Kaiser
Window (8)
OR
14.b. A cascaded realization of first order digital filter with
the system function of the (16) individual section are
H1(z)=1/(1-0.9z-1) and H2(z)=1/(1-0.8z-1).Draw the product
quantization noise model of the system and determine the overall
output noise
power.
15.a.i) Explain about Speech Compression
(8) ii) Find the IDFT of a sequence
X(k)={5,0,1-j,0,1,0,1+j,0}
(8)
OR
15.b.i) Derive the frequency response of a linear phase FIR
filter when impulse
(8) response is Antisymmetric and N is odd ii)Obtain the
transversal structure and linear phase realization structure for
the system
H (z) =1/2+1/4z-1+1/4z-2+1/2 z-3
(4) iii) Obtain cascade realization using the minimum number of
multipliers
H(z)=(1+1/2z-1+z-2)/(2+1/4 z-1+2 z-2 )
(4).
