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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC SEMESTER-VI EXAMINATION WINTER 2018
Subject Code:X61103 Date: 27/11/2018
Subject Name: Digital Signal Processing
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Draw three different sketches illustrating the periodic sampling of a low-pass signal with band-width in frequency-domain with three different situations arising due to the sampling rate and the band-width B. If the bandwidth of the low-pass signal to be sampled is B=4kHz, then what should be the period of the sampling? Why, give justification from the sketched you have drawn.
07

What are the conditions to be followed by LTI (Linear Time-Invariant) systems? Based on your answer, verify that the following two systems are LTI or not, give justification in each case:
a
where is the input signal and is the output signal.
07
Q.2

A LTI system is represented by its impulse response, given as 1}. Calculate the output signal of the given LTI system, if the input signal is 4}. Also represent the given LTI system in form of constant coefficient difference equation.
07

State and derive (Step by Step) the DTFT (Discrete Time Fourier Transform) theorem regarding the multiplication of two signals in time-domain.
07
OR

Determine the z-transform of the overall system that is created by series connection of two LTI systems given by their constant coefficient difference equations as given below:
System-1 0.2
System-2 0.3
Also specify the RoC (Region of Convergence) in z-plane for the overall system if the system has to be a causal system.
07
Q.3

Determine the constant coefficient difference equation for a system given by the z-transform, 1 RoC by applying the inverse z-transform methods.
07

Give Direct form-I and Direct form-II realizations for a system given by a linear constant coefficient difference equation as,
0.1 0.2 0.5
07
OR
Q.3

Explain various types of symmetry conditions for LTI systems to have linear phase response.
07
2

Explain with appropriate diagrams, Transposed Forms for realization of IIR filters.
07
Q.4

Explain the impulse invariance method of approximation in discrete-time from continuous time IIR filter design.
07

Explain the windowing method for design of FIR filters in discrete-time.
07
OR
Q.4

Explain the bilinear-transform method of approximation in discrete-time from continuous time IIR filter design.
07

Explain the N-point DFT (Discrete Fourier Transform) with details of equations. What is the effect of number of points (N-point) on the interpretation of DFT?
07
Q.5

Calculated the 4-point DFT of the sequence given as 7}. Also calculate the 8-point DFT of the same sequence but with zero-padding. Compare both the 4-point DFT and 8-point DFT of the same sequence.
07

Sketch the signal flow diagram for the radix-2 DIT (Decimation-In-Time) FFT (Fast Fourier Transform) algorithm for 8-point DFT.
07
OR
Q.5

Perform Linear Convolution of the following two sequences by applying DFT based method: 1}. How many point DFT you should do for this purpose? Compare your answer with straight method of convolution.
07

In context of DSP processors
Explain the concept of pipe-lining with neat diagram.
Clear the difference between the architectures of Fixed point DSP Vs. Floating point DSP
07