Digital Signal Processing — Winter 2021

What are the basic operations on discrete time signal. Explain with suitable example and graphical representations.

Find whether the following signal are energy, power signal, neither energy nor power signal. Calculate the power and energy in each case. 𝜋 x(n) = sin( n)3

Find the convolution of the signal 2 n = −2,0,1 x(n) = {3 n = −1 0 elesewℎere Using graphical method and Analytical method

Check whether following system are a. Static or dynamic b. Linear or Non linear c. Causal or non causal d. Shift variant or non variant Y(n) y(n) = log |x(n)|10

State and prove the time shifting and frequency shifting properties of DTFT

What is the input signal x(n) that will generate the output sequence y(n) ={1,1,2,0,2,1} for the system with impulse response h(n) ={1,-1,1}

Find the response of the system described by the difference equation y(n)+2y(n−1)+y(n−2) = x(n)+x(n−1) n1 For the input signal x(n) = ( ) u(n) with initial condition y(-1) =y(-2)=12

Derive the property of Time convolution and Tine shifting of Ztransform

Describe the limitation of Direct form I. Compare Direct form Iand Direct form II structure realization for FIR filter design

Using long division method determine inverse Ztransform of the following z2+2z X(Z) = ROC |z| > 1 z3−3z2+4z+1

State and prove Parseval’s theorem for discrete aperiodic signal

Derive differentiation property of Zdomain

Find the z transform of the sequence also find out its ROC 1 n 𝜋n x(n) = ( ) cos( )u(n)43

Find Inverse Discrete Fourier transform(IDFT) of X[k] = {4,2,0,4} using DFT algorithm

Realize the system given by the difference equation y(n) = −0.1y(n−1)+0.72y(n−2)+0.7x(n)−0.252x(n−2)in parallel structure realization.

Find the 8 point DFT of x(n) ={1,1,0,0,0,0,0,0}. Use the property of conjugate symmetry.

Find Inverse Discrete Fourier Transform (IDFT) using Decimation In Time radix 2 (DIT-FFT) algorithm X[k] ={1, 1-2j,-1,1+2j}

Realize the system with difference equation using cascade structure realization311 y(n) = y(n−1)− y(n−2)+x(n)+ x(n−1)483

Perform the circular convolution of following sequence using DFT and IDFT formula x1(n) ={1,2,1,2} and x2(n) ={4,3,2,1}

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

Consider a ramp sequence and sketch interpolated and decimated version with the factor of 3. nu(n)for n ≥ 0 r(n) = { 0, elsewℎere

For analog transfer function2 H (s) = a (s+1)(s+3) Determine H(z) if T =1s using impulse invariance method

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

Define multirate system. Where multirate digital signal processing require? What are the advantages of multirate signal processing?

Adigital filter with 3dB bandwidth of 0.4π is designed from the analog filter whose system response is Ω c H(s) = s+Ω c Use the bilinear transformation and obtain H(z)