NODIA AND COMPANY. Model Test Paper - I GATE Signal & System. Copyright By Publishers
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1 No part of tis pubicatio may be reproduced or distributed i ay form or ay meas, eectroic, mecaica, potocopyig, or oterwise witout te prior permissio of te autor. Mode Test Paper I GATE Copyrigt By Pubisers Iformatio cotaied i tis book as bee obtaied by autors, from sources beieves to be reiabe. However, eiter Nodia or its autors guaratee te accuracy or competeess of ay iformatio erei, ad Nodia or its autors sa be resposibe for ay error, omissios, or damages arisig out of use of tis iformatio. Tis book is pubised wit te uderstadig tat Nodia ad its autors are suppyig iformatio but are ot attemptig to reder egieerig or oter professioa services. NODIA AND COMPANY B8, Dasree Tower Ist, Cetra Spie, Vidyadar Nagar, Jaipur 009 P : emai : equiry@odia.co.i Prited by Nodia ad Compay, Jaipur
2 Q. Q. 5 carry oe mark eac. Q. A Causa Sequece x6@ as te trasform b X ^ = 6 ^ ^ 5 If a ew sequece y6@ = a x is formed, te wat wi be te vaues of a for wic te sequece y6@ is miimum pase? (A) a < (B) a < 6 5 (C) a < (D) No possibe vaues Q. Cosider a fuctio x^t avig te Lapace trasform give by Xs = s + ^ ; < Re s < s + 5s + 6 ", Te fuctio x^t equas to t u t t (A) e u^ t+ e u^t (B) e u^t+ e u^t t t (C) e u^te u^t (D) Noe of tese Q. Let a fuctio xt ^ = ut ^ ut ^ T/ + ut ^ T. If we approximate te fuctio xt ^ by gt ^ = csi t, 0 < t < T, te te best approximated vaue of c wi be (A) p (C) 4p (B) p (D) 4 p Q.4 Cosider te foowig differetia equatios. d y^t dy^t (i) + a + ayt = ut ^ ^ yt ^ dyt ^ (ii) + ayt = aut dt ^ ^ (iii) d y^t dy^t + t + tyt = 5 ^ Wic of te above represets te iear system (A) (i) ad (ii) (C) (i) ad (iii) (B) (i) oy (D) (ii) ad (iii)
3 Q.5 Te Lapace trasform of a fuctio f^t is give by Fs ^ = 5s + ss ^ + s+. Te vaue of im f ^ t is t " (A) / (B) 5/ (C) Ca ot be determied (D) Q. 6 Q. 5 carry two marks eac. Q.6 Cosider a siga y^t reated to x^t ad x^t as yt ^ = x^t* x^ t+ were x^t= e t u^t, x^t= e t u^t Te Lapace trasform Y^s wi be s s (A) e e c s + mb s (B) s e s s e c + mb s (C s e s s e s c + mb (D) s e s s e s c + mb + Q.7 Wat wi be te trasform of te siga x = b u+ (A) (C) b b, > / (B), > / (D) b b, < /, < / Q.8 Matc te sytem equatio to its correspodig type of system ad coose te correct optio. System Equatio Type of system dyt ^ dy^t (P) Liear ad time variat (i) + + yt = txt ^ ^ (ii) y^t= xt ^ (Q) Liear ad time ivariat (iii) y^t= x^t (R) Noiear ad time variat (S) Noiear ad time ivariat (A) (i)p, (ii)s, (iii)p (B) (i)p, (ii)r, (iii)q (C) (i)q, (ii)s, (iii)p (D) (i)q, (ii)r, (iii)p
4 Q.9 Wat wi be te discrete time Fourier trasform for te siga x 6@ = 8,, 0,, B (A) j^si w+ si w (B) j^siw+ siw (C) ^cos w+ cos w (D) ^cos wcos w Q.0 Cosider te foowig statemet about discrete LTI system wit frequecy respose He ^ jw ad impuse respose 6@ jw. He ^ = H* ^e jw. System is causa. DTFT of frequecy 6 is imagiary Wic of te foowig is correct correspodig to above statemets. (A) 6@ is rea ad + ^ is eve (B) 6@ is rea ad + ^ is odd (C) 6@ is imagiary ad eve (D) 6@ is imagiary ad odd Q. Wat wi be te uit step respose of a causa system for wic te trasform of te impuse respose is H = ^ < 4F (A) u6@ / d64k@ (B) u6@ / d644k@ (C) u6@ / d644k@ (D) u6@ / d64k@ Numerica Aswer Questios Q. Wat is te Nyquist rate (i H) of te siga xt si 00 t ^ = b pt p? Q. Wat wi be te Nyquist sampig rate (sampes/secod) for te siga x^t = si c^00tsi c ^000t?
5 Commo Data Questios Commo Data for Questios 4 ad 5: A causa iear time ivariat system as te system fuctio H = a ^, were a is rea a Q.4 Te give system H^ is (A) A Pass System (B) Miimum Pase System (C) Stabe for vaues of a > (D) Low Pass System Q.5 Wat wi be te impuse respose of system? (A) au a a ^ u (B) a u a u (C) au u (D) a a u6@ END OF THE QUESTION PAPER For detaied Soutios of tis test paper pease mai to equiry@odia.co.i. Pease metio your Name, Coege, Graduatig Year ad GATE Registratio Number i te mai.
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