Digital signal processing JAN 2014

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Question Paper for PGICE-13 Batch of M.Tech 1st Semester at Sant Longowal Institute of Engineering and Technology, Longowal.

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Digital signal processing JAN 2014

  1. 1. >c, _.a= .*'3e, :<u Minor-I Class: PGIICEI 13 Subject Code: IE-8104 Subject: Digital Signal Processing Max. Marks: 30 Q. l a) How does digitalsignal processing affect the performance of the system? _ b) Explain the concept and importance of correlation. How the correlation can be found with convolution machine? c) (i) Show that the fundamental period Np of the signals sk(n) = exp(j27tkn/ N) =0_.1 ,2. . is given by N, ,= N/ GCD(k, N) where GCD is the greatest common divisor of k and N. (ii) What is the fundamental period of this set for N=7 & N= l6. Q.2 a) Detennine the direct form -II realization for each of the following LTI systems. i) 2>'[n] + Yin-1] - 4Y[n-3] = Xlnl + 3X[n-5] ii) y[n] = x[n] — x[n-1] +2x[n-2] — 3x[n-4] b) Determine and sketch the convolution y[n] of the signals x[n] = 1/3) n 0 5 n 56 {O elsewhere h[n] = 1 -2 sn 5 2 0 - elsewhere Q.3 a) Show that the output of an LTI system can be expressed in terms of its unit step response s[n] as follows go y[n] = Z [S[1<] -Slk-1]]X[I1-kl .1-§ £ = Z [X[1<] -Xlk-1]]S[n-kl 5,; , £3 b) Compute the correlation sequence rx, (l) of the following sequences X[nl= [1 no'NSnSno+N 0 elsewhere y[n] = 1 - N 5 n S N O elsewhere . :‘7“A£, t)oL{€Cl lrLiJO‘‘, o‘i. (. Lw» ' l"! _ 1., ch Lat ~; “,‘, “G§_k, "
  2. 2. '‘/ ’<lLE--l3(¢»33l [ 5 l; in‘ rVQ S40 1' Lu ifvx l -'; l7<: ’cL 1 Sant Longowal Institute of Engineering and Technology, Longowal Subject code : |E»8104 Subject: Digital Sigrial Processing Class: M. Tech Max Marks: 30 Q.1 al Explain the response of LTl system to complex exponential in terms of eigen function and explain . its importance in analysis of LTI system. b)'A discrete time periodic signal x[n] is real valued and has a fundamental period N=5.The non—zero Fourier coefficients fior x[n] are a, = 2, all: a_z = Zexpljn/6), a4: a. ,. = exp(jn/3) (1.2 Determine the Fourier series coefiicients for each of the following discrete time periodic signal. a)x[n] = sin (2110/3)COS(TU1/V2) b) x[n] periodic with period 4 x[n] = 1—sin(nn/4) for O 5 n 5 3 c) x[n] periodic with period 12 x[n] : 1~sin(nn/ zl) for 0 5 n 5 11 ‘ Q.3l Find the FT of following signals a) x[n] : sin(nn/2) +cos(n) I b) x[n] = (1/2)" cos((n/8)(n~1)) _/ C) x[n] = u[n—2] _— u[n-6]
  3. 3. l70illcEll3€s. !( _(/ fin, Sant Longowal Institute of Engiueerlng and Technology. Longownl Subject Code: IE-8l04 Subject Name: Digital Signal Processing Class: PG/ ICEII3 Max. Marks. 50 Note: First question is compulsory. Attempt any two iuestions from part-A and part-B each. Q. l a) When discrete time signals are called as periodic signals? b) Define even and odd signals. c) Define Quantization. d) What is zero padding e) Detennine the value ofWl6 for 64-point DFT. I) Find the values ofVNk , When N=8, k=2 and also For | =3 g) List two properties oFDTFT. It) What is the relation between Z domain and laplucc transform .7 i) Write the characteristics feature of Hanning window j) Z-transform is reduced to Fourier traiisforin when evaluatctl a; which points’? (IOK l : I 0) Part-A 0.2 a) Realize the following system in cascade form H (2) = (i-z". z'= )/ (z'”-3z«i) (z-l) b) Realize the following system in direct form I and II for H(z)= l / (i+. i.z"+a, z‘3) ( 10) Q3 Find the inverse z-transform for the sequences /4!) i+3z"/ i+3z“+2z'= b) i+2z"/ i+z* c) 2 ‘+1’. l-z" 0.4 For an LTI system with impulse response h[n] = (I/2)" u[n] ([0) Use fourier transform to detennine the response to c. ic| i oftue following input signals i) x[n] = (3/4)" ti[n] ii) x[n] = (n4 l)(l/1.. (ii) iii) x[n] = (-I)" ([0) Part-B Q5 La) Define DFT and IDFT. List Circular convoltitioi Circular conelation and Time reversal properties of DFT. b) Find the [DFT oflhe sequence ‘< (K) = (2, 2-33. 4, 2+3)‘; (,0, 0.6 0.5 La) Compute the DFT using Radix-2, DIT-FFT ulgorithnt x(n)= l l. |.l. l.0.0.0,0) b) Draw the Butterfly diagram for a 16-bit DIF-FFT algorithm 0.7 .11) Compare Butterworth and Chebyshev approximation techniques of filter designing. b) Design a Digital Butterworth LPF using Dilinear transfonnation technique for the following specifications: 0.707:lH(w)l'; I :0<_w: '0.2n ll-l(w)| S0.08:0.41t, <_-wgn ('0) ((~_{‘, p1j 4 6,1 ‘ rib, Q) ‘twat . c, «_; ~ i~_ M, 'l cl: ‘- ”l~: ” 5#‘1v('? .‘l»(‘~ 1;, ‘MT. , -.u. ..aa_-. =.1~ , ... 3.. at

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