Digital Signal Processing — Winter 2021

Attempt following questions. 1) Explain architecture for Digital Signal Processor with its key features in detail.

Classify the following systems. 1) Static Vs Dynamic systems 2) Recursive Vs non-recursive systems 3) Linear Vs non linear systems 4) Time Variant Vs Time Invariant systems

Determine convolution of given discrete time sequences with graphical approach. x(n) = {3,11,7,0,-1,4,2} for n = -3 : 3 and h(n) = {2,3,0,-5,2,1}for n= -1:4.

Determine impulse response of following LTI systems described by the following second order difference equation. y(n) - 3y(n-1) - 4y(n-2) = x(n) + 2 x(n-1)

Discuss various properties of DTFT. Also compare DTFT with DFT. Why DFT is better?

Discuss following properties of Z-Transform in detail with proof. 1) Convolution 2) Differentiation 3) Time Shifting

Describe the properties of ROC in context with Z-Transform and determine the Z-Transform of given signal. x(n) = u(n) – u(n-20)

What is the need of Transformation on any signal? Compare Z Transform with DFT and FFT with examples.

Determine Partial Fraction Expansion of X(z) = (1 +z-1) / (1- z-1+0.5 z-2)

Compute Circular convolution of following discrete time sequences. x(n) = {1,2,2} and h(n) = {1,2,3,4}

Obtain direct form I & II, cascade and parallel form structures for the given system y(n) = ½ y(n-1) + ¼ y(n-2) +2 x(n) - x(n-1)

Justify the following statement: Multiplication of Two DFTs is circular convolution in Time Domain. Derive relevant equations.

Compute 4 point DFT of a given discrete sequence using Radix-2 DIF FFT1 algorithm. x(n) = { 1,2,3,4 }

Explain Radix 2 DIT FFT algorithm for computing 8 point DFT. Derive all necessary equations and signify importance of bit reversal table in it.

List out benefits of Digital filter over Analog filters. Discuss parameters and their importance in designing any practical frequency selective filter.

Discuss BLT with regard to IIR filter design. Why is it more efficient than Impulse Invariance approach?

How FFT is computationally more efficient than DFT? Under which set of parameters comparison between these algorithms are possible? Comment on efficiency of FFT against DFT.