Digital Signal Processing — Winter 2019

Define the following terms in context of signal processing: (1) Period of discrete sinusoid, (2) Correlation of signals, (3) ROC of Z-transform.

The system given below have input x(n) and output y(n). y(n) = log {x(n)} Answer the followings with justification. (1) Is the system linear? (2) Is it time-invariant? (3) Is it stable?

Draw & discuss typical block diagram of Digital Signal Processing (DSP). Explain any one example of DSP used in real-time application.

Explain the following terms in brief: (1) Minimum phase system. (2) Dirichlet’s Condition for existence of DTFT.

State the relationship between Z-transform and Fourier transform. Determine the step response of the causal system described by the following LCCDE. y(n) = y(n−1)+x(n) Consider x(n) as input and y(n) as output of the system.

Compute the linear as well as circular convolution of following sequences: x(n) = {1,2,0,1} and ℎ(n) = {2,2,1,1} for 0 ≤ n ≤ Comment on the results obtained.

Aliner time-invariant system is characterized by its impulse response 1 n ℎ(n) = ( ) u(n)2 Determine the spectrum and energy density spectrum of the output signal when the system is excited by the signal. 1 n x(n) = ( ) u(n)4

Compute the Z-transform of the following sequence. x(n) = a|n|;0 < a < 1

Draw Direct Form-Iand Direct Form-II structures for the following system function:1 1+0.875z−1 H(z) = (1+0.2z−1 +0.9z−2)(1−0.7z−1)

Write down the properties of Z-transforms and prove the followings: (1) Time-shifting property (2) Differentiation property

Compute the DFT of the following four-point sequence using DFT matrix. x(n) = {0,1,2,3}

Consider the signal x(n) = {−1,2,−⏟3,2,−1} ↑ with Fourier transform X(𝜔). Compute the following quantities, without explicitly computingX(𝜔). (1) X(0) (2) X(𝜋) (3) ∫ 𝜋 |X(𝜔)|2 d𝜔 −𝜋

List out the properties of DFT and prove the followings: (1) Symmetry for real sequence (2) Time reversal

Enlist atleast three differences between FIR and IIR Filters.

Explain the followings in context of Multirate signal processing: (1) Decimation (2) Interpolation

Discuss the design of FIR filter using windowing method in brief.

What do you mean by frequency wrapping?

Explain the followings in context of DSP processor architecture: (1) MAC (2) Pipelining

Discuss design steps of IIR filter using bilinear transformation.

Compute the IDFT of the function X(𝜔) = 2𝜋 𝛿(𝜔)

Write a short critical note on adaptive filters and discuss any one application of it.

Discuss in brief: Radix-2 Decimation-in-Time FFT algorithms.

Determine the partial-fraction expansion of the proper function X(z) = 1− 1.5z−1+ 0.5z−2

Write a short critical note on Harward architecture of DSP processor.

Explain in brief: The Goertzel Algorithm.