M.Sc. (Semester III) (CBCS) Examination Nov/Dec-2018
Electronics
DIGITAL SIGNAL PROCESSING
Time: 2½ Hours Max. Marks: 70
Instructions: All questions are compulsory.
Use of Log table and calculator is allowed.
Draw neat and labeled diagram wherever necessary.
Figures to the right indicate full marks.
Q.1 Choose the correct answer: 14
What is the z-transform of the finite duration signal
x n
↑
2 4z 5z2 7z3 z4 2 4z 5z2 7z3 z5
2 4z−1 5z−2 7z−3 z−5 2z2 4z 5 7z−1 z−3
Which of the following is a method for Implementing an FIR system?
Direct form Cascade form
Lattice structure All of the mentioned
and are an N-point DFT pair, then X(k

None of the mentioned
If the signal to be analyzed is an analog signal, we would pass it through an
anti-aliasing filter with B as the bandwidth of the filtered signal and then the
signal is sampled at a rate:
Fs 2B Fs B
Fs 2B Fs 2B
None of the mentioned
Which of the following method is used to find the inverse z-transform of a
signal?
Counter integration Expansion into a series of terms
Partial fraction expansion All of the mentioned
Which of the following is true regarding the number of computations required
to compute an N-point DFT?
N2 complex multiplications and N complex additions
N2 complex additions and complex multiplications
N2 complex multiplications and complex additions
N2 complex additions and complex multiplications
In Overlap save method of long sequence filtering, how many zeros are
appended to the impulse response of the FIR filter?
L+M L
L+1 L-1
Which of the following is a digital-to-analog conversion process?
Staircase approximation Linear interpolation
Quadratic interpolation All of the mentioned
10) What is the ROC of a causal infinite length sequence?
z z
r2 z None of the mentioned
11) If is a real valued sequence of 2N points and and
then what is the value of k
X1 k −W2/kNX2 k
X1 k +W2/kNX2 k
X1 k +W2/kX2 k
X1 k −W2/kX2 k
12) A signal has a Fourier transform If is a real and odd function
of them is
A real and even function of ω
An imaginary and odd function of ω
An imaginary and even function of ω
A real and odd function of ω
13) For a signal the Fourier transform is Then the inverse Fourier
transform of is given by
3t e−i4πt
14) What is the set of all values of z for which attains a finite value?
Radius of convergence Radius of divergence
Feasible solution None of the mentioned
Q.2 Attempt any four of the following questions. 08
Determine the Z-transform of
What is the mathematical problem involved in the design of window
function?
What is meant by radix-2 FFT? The FFT algorithm is most efficient in
calculating N-point DFT.
Explain development of Fourier transform.
What is mean by sampling? State the sampling theorem.
Write a notes on (Any Two) 06
Bilinear transformation
Aliasing Anti-aliasing problem
DIF algorithm
Q.3 Answer any two of the following questions. 08
State and prove Initial value theorem property of z-transform.
State and prove periodicity property of DFT.
State and prove scaling property of Fourier transform.
Answer any one of the following questions. 06
Determine the length 4 sequence from its DFT. 1+j
Obtain inverse Z-transform of
for 0.5 using long
division method.
Q.4 Answer any two of the following questions. 10
Find the Fourier transform of a rectangular pulse 2 seconds long with a
magnitude of 10 volts.
x1 n 4 and x2 n
Find the linear convolution of and x2 using Z-transform.
↑ ↑
An analog filter has the following transfer functions using
bilinear.
Answer any one of the following questions 04
Differentiate between z-transform and DFT.
Find Fourier transform and sketch the magnitude spectrum of unit
impulse function.
Q.5 Answer any two of the following questions. 14
Compute the 8-point DFT of a sequence, 0
using in place radix-2 decimation in time FFT algorithm.
Develop direct form -II realization for the digital filter with transfer function
− − 0. −
Find the Fourier transform of sinusoidal pulse shown in figure