Define discrete time signals. Enlist classification of Discrete time signals.
[3 marks]Determine whether or not the following signals are periodic. In case a signal is periodic, specify its fundamental period
[ marks]1 x1 ( n ) s in2 n c o s2 n = + (ii)2 ( ) c o s2 c o s (3 ) x n = n n04
[ marks]ClIa.s sify following systems as : (a) Causal or non-causal; (b) Linear or nonlinear and (c) shift invariant or shift variant
[7 marks]y (n)= Log x(n)110 (ii) y (n)= x(n)x(n−4)2
[ marks]Exp(liaiiin) Dirichlet’s Conditions for existence of Fourier Transform.
[3 marks]State formulas for Discrete Time Fourier Transform (DTFT) Z-transform of discrete time signal x(n). Prove relationship between Z-transform and DTFT.
[4 marks]Acausal LTI system is described by following difference equation: y ( n ) − y ( n − 1 ) − y ( n − 2 ) = x ( n ) + 2 x ( n − 1 )07 Find (a) system function (b) Frequency response. (c) Plot pole zrod and Specify ROC of H(z). (d)determine whether the system is stable or not.
[ marks]Determine response of the systems having input x(n) and inpulse response h(n) using (a) linear convolution and (b) circular convolution. x ( n ) = { 1 ,2 ,3 , 4 } and h ( n ) = { 1 ,1 ,1 ,1 }07
[ marks]Prove that for causal sequences, the ROC of Ztransform is exterior of a circle of radius r.
[3 marks]Find Direct Form-II structure for the following system function: 3z3 −5z2 +9z−3 H(z)= [z− 1 ][z2 −z+ 1 ]23
[4 marks]A Causal LTI system is described by the difference equation2 y ( n ) +1 y ( n − 1 ) = x ( n ) +1 x ( n − 1 )07 Determine System function of the system and give ROC. Find unit sample response of the same. Find the magnitude response of the same.
[ marks]Using properties of Ztransform, compute Ztransform for following signals. x ( n ) = 2 n u ( n − 2 )03
[ marks]State and prove Time reversal property of Ztransform.
[4 marks]Using partial fraction expansion, discuss all possibilities of ROCs and obtain all possible signals of the following: X ( Z ) = [ 1 − (1 ) ( z1 − 1 ) ] z [ 1 − 1 − (1 ) z − 1 ]07
[ marks]Compute the 4 point DFT of the following four-point sequence using DFT matrix. x(n)= {2,3,3,1}
[3 marks]Explain advantages of using multi-rate signal processing. Explain Decimation or Interpolation concept by taking simple suitable example.
[4 marks]Discuss 8-point Radix-2 Decimation-in-Frequency FFT algorithm.
[7 marks]Find 4-point DFT of x(n)- {1,-1,2,-2}, directly using equation .
[3 marks]List out the useful properties of DFT and prove any one of them.
[4 marks]Discuss 8-point Radix-2 Decimation-in-time FFT algorithm.
[7 marks]Define an adaptive filter. Draw (only a block diagram) that explains any one application of adaptive filters.
[3 marks]Explain in brief on Harvard architecture of DSP processor.
[4 marks]Explain with necessary details design of IIR filter by approximation of derivatives transformation method. Explain with justification how it is NOT better than bilinear and impulse invariance methods.
[7 marks]Enlist differences between FIR and IIR Filters.
[3 marks]Explain the followings in context of DSP processor architecture: (1) MAC (2) Pipelining
[4 marks]Find the order and cut -off frequency of a IIR butter worth digital filter with the following specifications. Use impulse invariant method and take sampling period T=1 second. 3 0 . 8 0 H ( w ) 1 . . . f o r _ 0 w 0 .207 H(w) 0.20..for_0.32 w.
[ marks]