Digital Signal Processing — Summer 2022

Explain the following with example: (1) Continuous valued signal (2) Discrete valued signal

State sampling theorem. What is the relation between frequency in discrete time domain and frequency in analog domain?

Sketch the discrete time signal x(n)=2-n for -2≤n≤2 and obtain: (1) y = 2x(n)+𝛿(n)1 (2) y = x(n).u(2−n)2

Explain the distinct features of DSP Processor.

Compute the DFT of the four point sequence x(n)=(0 1 2 3)

Perform the circular convolution of the following two sequences graphically: x (n) = {2,1,2,1}1 ↑ x (n) = {1,2,3,4}2 ↑

Determine the response of the FIR filter using DFT, with impulse response ℎ(n) = {1,2,3} to the input sequence x(n) = {1,2,2,1}

Determine if the system described by following input-output relation is linear or non-linear: y(n)=n x2(n)

Determine the stability and causality of the given system: y(n)=x(2n)

The impulse response of a linear time-invariant system is h(n)={1,1,1}. Determine the response of the system to the input signal using convolution with graphical method for x(n)={1,2,1,2}

Determine whether the given sinusoid x(n)=cos0.01πn is periodic or not. In case it is periodic specify the fundamental period.

What is correlation? Mention types of correlation and its applications.

Determine the homogeneous solution of the system described by y(n) - 3 y(n-1) - 4 y(n-2) =x(n)

Find the Z-transform and ROC of x(n)=nu(n). where u(n)is unit step sequence.1

Find the inverse Z-transform using partial fraction expansion:1 X(z) = (1+z-1)(1-z-1)2

Using Z-transform method obtain impulse response of a system described by: y(n) = 2.5y(n−1)+x(n)

Find Ztransform and ROC of following signal : x(n) = (-3)n u(-n-1)

1- 1 Z-1 Find the inverse z-transform of X(Z) = 2 |Z| > 1/2 using 1- 1 Z-24 power series expansion method.

A Linear Time Invariant system is characterized by the system function 3+4z−1 H(z) = 1−3.5z−1 +1.5z−2 Specify the ROC of H(z) and determine h(n) for the following conditions:

The system is stable

Explain the advantages of IIR filter over FIR filter.

Consider the causal Linear Time Invariant system function 1+z−1 H(z) =1 (1−0.5z−1 + z−2)(1+0.25z−1)3 Draw Direct form-II structure for IIR filter.

Explain Radix-2 decimation in time algorithm in detail.

Compare merits and demerits of DSP over ASP.

The transfer function of discrete time causal system is given by 1−z−1 H(z) = 1−0.2z−1 −0.15z−2 Draw cascade realization for IIR filter.

Convert the analog filter with system function s+0.1 H (s) = a (s+0.1)2 +16 Into a digital IIR filter by means of the bilinear transformation. The digital filter is to have a resonant frequency of ω =π/2. r