M.Sc. (Semester III) (CBCS) Examination Mar/Apr-2018
Electronics
DIGITAL SIGNAL PROCESSING
Time: 2½ Hours
Max. Marks: 70
Instructions: Attempt five questions. Q. and are compulsory. Answer any three questions from Q.3 to Q.7. Figures to the right indicate full marks.
Q.1
Choose the alternatives given below.
08
If is causal sequence then its initial value is
x 0 =limz→∞X(Z)
x 0 =limz→0X(Z)
x ∞ =limz→1X(Z)
x ∞ =limz→1X Z (1−Z−1)
If is causal sequence then ROC is .
Interior part of circle of radius
Exterior part of circle of radius
Intersection of two circles of radii
Entire Z plane except
The low pass butterworth filter provides the magnitude response is nearly
Constant at lower frequency
equal to 1 at lower frequency
constant at higher frequency
both a and b
In the Z plane if pole is outside the unit circle then
The amplitude of the signal is increasing
The amplitude of the signal is decreasing
The amplitude of the signal is fixed amplitude
signal alters the sign
The modulation property of Fourier Transform F{x t ejωt} is
X(ω−ω0)
X(t−t0)
ejωtX(ω)
jω
The impulse invariance method is not suitable to design
low pass filter
high pass filter
band pass filter
digital filter
The necessary condition for to have fourier transform are
has finite number of discontinuities
is absolutely integrable over
has finite number of maxima and minima in every finite interval.
all above
Z-transform of delayed unit impulse signal is
ZK
Z-k
1
none of these
Page 2 of 2
SLR-UJ-330
State True or false.
06
The digital filter is stable if the poles are inside the unit circle in Z domain.
There is no aliasing effect in bilinear transformation.
Inverse fourier transform of is 1
The circular frequency shift property of DFT is also called Quadrature Modulation theorem.
Because of the non-linear mapping the amplitude response of digital IIR filter is expanded at higher frequencies and compressed at lower frequencies.
Auto-correlation is denoted by rxy(1)
Q.2
Attempt any two.
10
Find the Fourier Transform of signum function.
Explain the relationship between Z Transform and Fourier Transform.
With block diagram, explain the process of analog to digital conversion.
What is FFT? Explain Radix- 2FFT algorithm.
04
Q.3
State and prove that complex conjugate property of DFT.
08
Use the four point of DFT and IDFT to determine the circular convolution of sequences.
and
06
Q.4
Compute the DFT of sequence cos where N=4. Using DIF FFT algorithm.
08
Find the Z transform and sketch ROC for following sequence
2nu[n] 3n
06
Q.5
Determine the sequence associated Z Transform given below using partial fraction expansion method
(4Z2 5Z2 8Z Right sided sequence
08
State and prove final value theorem of z-transform
06
Q.6
Find out using impulse invariance method at 5 Hz sampling frequency from as given by
08
Write a note on:
FIR filter design using Kaiser window
Bilinear transformation for IIR filter design
06
Q.7
State and prove time differentiation property of Fourier transform.
08
Find the Fourier transform of sinusoidal pulse shown in figure 1
06