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Signals & Systems, 1. Basic operation on Signals, Q.1, , Consider a signal f (t ) as shown in figure, f (t ), , 2, 1, -2, , 2, , 1, , 0, , t, , The plot of signal f (4 − 2t ) is, , f (4 - 2t ), (A), , f (4 - 2t ), , (B), , 2, , 2, 1, , 1, -1 - 1 0, 2, (C), , 1, , t, , f (4 - 2t ), , (D), , 2, 1, 0, , -4 - 7 -3, 2, , -5, , t, , 0, , f (4 - 2t ), , 2, 1, , 3, , 1, , 2, , 2, , 3, , t, , 0, , 3, , 7, , 2, , 4, , 5, , t, , +∞, , Q.2, , The value of, , e, , −t, , δ(2t − 2)dt , where δ(t ) is the Dirac delta function, is, , [GATE EE 2016-Bangalore], , −∞, , Q.3, , (A), , 1, 2e, , (B), , 2, e, , (C), , 1, e2, , (D), , 1, 2e2, , 1, | t |≤ 2 , Consider signal x(t ) = , . Let δ(t ) denote the unit impulse (Dirac-delta) function. The value of the integral, 0 | t |> 2 , , , , 5, , 0, , 2 x(t − 3)δ(t − 4)dt is, , [GATE IN 2018-Guwahati], , (A) 2, , (B) 1, , (C) 0, , (D) 3, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Signals & Systems : GATE 2021-22 [EC/EE/IN], , 2, Q.4, , GATE ACADEMY®, , The integral, ∞, , 1, , [GATE IN 2011-Madras], , t e, 2π, , 2 −t 2 / 2, , δ (1 − 2t ) dt is equal to, , −∞, , (A), , 1, 8 2π, 1, , (C), , 2π, , e −1/8, , (B), , e −1/ 2, , 1, 4 2π, , e −1/8, , (D) 1, 2, , The value of the integral I = ( 5t 2 + 1) δ(t ) dt is, , Q.5, , 1, , (A) 0, , (B) 1, (D), , 125, 3, , (A) − (3 − π), , (B), , − (3 + π), , (C) 1, , (D) −1, , (C), , 42, 3, ∞, , Q.6, , [ESE EC 2013], , The value of, , (t, , 3, , + sin πt )δ '(t − 1)dt is, , −∞, , The complete even part xe (t ) of the signal x(t ) is, , Q.7, , (B), 2, , xe (t ), , (A), , -2, , 2, , -1, , 2, , (C), -2, , xe (t ), , 0, , 0, , t, , 1, , -2, , 1, , xe (t ), , (D), 2, , -1, , 2, -1, , t, , 1, , 0, , xe (t ), , t, , 1, -2, , 2, 0, , -1, , -2, , t, , 1, , -1, , Two periodic signals x(t ) and y (t ) have the same fundamental period of 3 seconds. Consider the signal, , Q.8, , z (t ) = x(−t ) + y (2t + 1). The fundamental period of z (t ) in seconds is, (A) 1, , (B) 1.5, , (C) 2, , (D) 3, , [GATE IN 2018-Guwahati], , 2π , The fundamental period of the signal x(t ) = 2 cos t + cos(πt ) , in seconds, is ________s., 3 , , Q.9, , [GATE IN 2015-Kharagpur], Q.10, , For a periodic signal v(t ) = 30sin100t + 10 cos 300t +6sin(500t + π / 4) . The fundamental frequency in rad/s is, [GATE EC, EE, IN 2013-Bombay], (A) 100, , (B) 300, , (C) 500, , (D) 1500, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Digital Electronics : GATE 2021-22 [EC/EE/IN], , 3, Q.11, , GATE ACADEMY®, , Consider the periodic signal, x(t ) = (1 + 0.5cos 40πt ) cos 200πt, where t is in seconds. Its fundamental frequency, in Hz, is, , Q.12, , (A) 20, , (B) 40, , (C) 100, , (D) 200, , [GATE IN 2007-Kanpur], , A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling, period Ts . In which one of the following cases is the sampled signal periodic?, , Q.13, , (A) T = 2 Ts, , (B), , (C) Always, , (D) Never, , [GATE EC 2016-Bangalore], , T = 1.2 Ts, , 301 , The fundamental period N 0 of the discrete-time sinusoid x[n] = sin , πn is_______, 4, , , [GATE IN 2016-Bangalore], Q.14, , A signal x(t ) = 5cos(150πt − 60) is sampled at 200 Hz. The fundamental period of the sampled sequence x(n) is,, [GATE IN 2004-Delhi], (A), , 1, 200, , (C) 4, Q.15, , 2, 200, , (B), , (D) 8, , A periodic time signal is given by x(n) = cos(3πn ) + sin(7πn) + cos(2.5πn), The term sin(7 πn) in x(n) corresponds to, , Q.16, , (A) 14th harmonic, , (B) 7th harmonic, , (C) 6th harmonic, , (D) 5th harmonic, , Consider the two continuous-time signals defined below :, t , −1 ≤ t ≤ 1, x1 (t ) = , 0, otherwise, , [GATE EE 2018-Guwahati], , 1 − t , − 1 ≤ t ≤ 1, x2 (t ) = , otherwise, 0,, , These signals are sampled with a sampling period of T = 0.25 seconds to obtain discrete-time signals x1[n] and x2 [n], , respectively. Which one of the following statements is true?, (A) The energy of x1[n] is greater than the energy of x2 [n], (B) The energy of x2 [n] is greater than the energy of x1[n] ., (C) x1[n] and x2 [n] have equal energies., (D) Neither x1[n] nor x2 [n] is a finite-energy signal., Q.17, , The mean square value of the given periodic waveform f (t ) is, , [GATE EE 2017-Roorkee], , f (t ), , 4, , -1.3, -3.3, , 0.7 2.7, -0.3, , 3.7 4.7, , t, , -2, , Q.18, , The energy of the signal x(t ) =, , sin(4πt ), is __________., 4πt, , [GATE EC 2016-Bangalore], , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Signals & Systems : GATE 2021-22 [EC/EE/IN], , 4, Q.19, , GATE ACADEMY®, , The waveform of aperiodic signal x(t ) is shown in the figure., , [GATE EC 2015-Kharagpur], , x(t ), 3, , -2, , 1, , 4, , -1, , -4, , t, , 2 3, -3, , t −1 , A signal g (t ) is defined by g (t ) = x , . The average power of g (t ) is _________., 2 , ∞, , Q.20, , The value of the integral, , sin c, , 2, , (5t ) dt is _____., , −∞, , [GATE EC 2014-Kharagpur], Q.21, , Q.22, , Q.23, , π, , The power of the signal s (t ) = 8cos 20π t − + 4sin(15π t ) is, 2, , , (A) 40, , (B) 41, , (C) 42, , (D) 82, , [GATE EC 2005-Bombay], , If the energy of the signal x(t ) is E x then what will be the energy for a signal x(at − b)?, (A), , Ex, a, , b, (B) E x, a, , (C), , 1, Ex + b, a, , 1, , (D) + b Ex, a, , , , A discrete variable is given by x(n) = (−1) n [u (n) − u (n − 3)], The energy of the signal is given by, , Q.24, , (A) 1, , (B) 2, , (C) 3, , (D) 6, , The power of a periodic signal shown in figure is, x(t ), , 4, , -5, , Q.25, , -2, , 0 2, -2, , 7, , 5, , (A) 56 unit, , (B) 8 unit, , (C) 11.2 unit, , (D) 32 unit, , t, , The periodic signal f (t ) shown in below figure. The power of signal x(t ) = − f (t ) is, f (t ), t3, -4, , -2, , t3, , 0, , 2, , 4, , 6, , t, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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5, , Digital Electronics : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , (A), , 64, 7, , (B), , 32, 7, , (C), , 256, 7, , (D), , − 32, 7, , Question 1, Check the following systems for, (A) Linear / Non-linear, (B) Time invariant / Time variant, (C) Static / Dynamic, (D) Causal / Non-causal, 1., y (n) = x(n − 3) + x(5 − n), , 2., , y (n) = x( n) cos ω0 n, , 3., , y (n) = x(n) + nx(n + 1), , 4., , y (n) = x( n) x(n − 1), , 5., , y (t ) =, , 6., , y (t ) = t, , 7., , y (t ) = t x(t ), , 8., , y (t ) = t ( x t ), , 9., , y (t ) = cos { x(t )}, , 10. y (t ) = x {sin t}, , 11., , y (t ) =, , 2. Systems, , d, x(t ) + 2 x(t ), dt, , 2t, , t, , , , 12. y (t ) =, , x ( τ) d τ, , −∞, , y (t ) =, , x ( τ) d τ, , 14. y ( n) =, , y ( n) =, , n +1, , x(k ), , 16. y ( n) =, , k =− ∞, , 17., , y ( n) =, , n, , x(k ), , k =− ∞, , −∞, , 15., , x ( τ) d τ, , −∞, , t /2, , 13., , d, x(t ) + 2 x(t ), dt, , 2n, , x(k ), , k =− ∞, , n, , x(k + 1), , k =− ∞, , Q.2, , Consider a continuous-time system with input x(t ) and output y (t ) given by, , y (t ) = x(t ) cos (t ), This system is, , [GATE EE 2016-Bangalore], , (A) linear and time-invariant, , (B) non-linear and time-invariant, , (C) linear and time-varying, , (D) non-linear and time-varying, 5t, , Q.3, , The system represented by the input output relationship y (t ) =, , x(τ) d τ, t > 0 is, , −∞, , [GATE EE 2010-Guwahati], , Q.4, , (A) Linear and causal, , (B) Linear but not causal, , (C) Causal but not linear, , (D) Neither linear nor causal, , The input and output of a continuous time system are respectively denoted by x(t ) and y (t ) Which of the following, descriptions corresponds to a causal system?, , [GATE EC 2008-Bangalore], , (A), , y (t ) = x(t − 2) + x(t + 4), , (B), , y (t ) = x(t − 4) + x(t + 1), , (C), , y (t ) = x(t − 4) + x(t − 1), , (D), , y(t ) = x(t + 5) + x(t − 5), , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Signals & Systems : GATE 2021-22 [EC/EE/IN], , 6, , GATE ACADEMY®, , Let x(t ) be the input and y(t ) be the output of a continuous time system. Match the system properties P1, P2 and, , Q.5, , P3 with system relations R1, R2, R3, R4., , [GATE EC 2008-Bangalore], , (Properties), P1 : Linear but not time-invariant, P2 : Time-invariant but not linear, P3 : Linear and time-invariant, (Relations), R1 : y (t ) = t 2 x(t ), , R2 : y (t ) = t | x(t ) |, , R3 : y (t ) = | x(t ) |, , R4 : y (t ) = x(t − 5), , (A) (P1, R1), (P2, R3), (P3, R4), , (B), , (C), , (P1, R3), (P2, R1), (P3, R2), , (P1, R2), (P2, R3), (P3, R4), , (D) (P1, R1), (P2, R2), (P3, R3), , The input and output of a continuous time system are respectively denoted by x(t ) and y(t ) Which of the following, , Q.6, , descriptions corresponds to a causal system?, , Q.7, , [GATE EE 2008-Bangalore], , (A), , y(t ) = x(t − 2) + x(t + 4), , (B), , y(t ) = x(t − 4).x(t + 1), , (C), , y(t ) = (t + 4).x(t − 1), , (D), , y(t ) = (t + 5).x(t + 5), , Which one of the following discrete-time systems is time-invariant?, (A), , y[n] = n x[n], , (B), , y[n] = x[3n], , (C), , y[n] = x[−n], , (D), , y[n] = x[n − 3], , [GATE IN 2008-Bangalore], , Consider a continuous time system A, modeled by the equation y (t ) = t x(t ) + 4 and a discrete time system modelled, , Q.8, , 2, by the equation y[ n] = x [ n]. These systems are, , [ESE EC 2015], , (A) A-time invariant and B-time invariant, , (B) A-time varying and B-time invariant, , (C) A-time invariant and B-time varying, , (D) A-time invariant and B-time varying, n, , 1, The discrete LTI System is represented by impulse response h(n) = u (n) , then the system is [ESE EC 2015], 2, , Q.9, , (A) Causal and stable, , (B) Causal and unstable, , (C) Non causal and stable, , (D) Non causal and unstable, t, , Q.10, , The input x(t ) and output y (t ) of a system are related as y (t ) =, , x(τ) cos(3τ) d τ . The system is, , −∞, , [GATE EC, EE, IN 2012-Delhi], , Q.11, , (A) time-invariant and stable, , (B) stable and not time-invariant, , (C) time-invariant and not stable, , (D) not time-invariant and not stable, , Consider a system with input x(t ) and output y (t ) related as follows, y (t ) =, , [GATE IN 2011-Madras], , d −t, {e x(t )}, dt, , Which one of the following statements is TRUE?, (A) The system is non linear, , (B) The system is time-invariant, , (C) The system is stable, , (D) The system has memory, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Digital Electronics : GATE 2021-22 [EC/EE/IN], , 7, Q.12, , GATE ACADEMY®, , A system with input x(t ) and output y (t ) is defined by the input-output relation, , y (t ) =, , −2t, , x(τ) d τ, , −∞, , The system will be :, , Q.13, , [GATE EE 2008-Bangalore], , (A) Causal, time-invariant and unstable, , (B) Causal, time-invariant and stable, , (C) Non-causal, time-invariant and unstable, , (D) Non-causal, time-variant and unstable, , 5 , A system with input x[n] and output y[n] is given as y[n] = sin π n x[n], 6 , The system is :, , Q.14, , [GATE EC 2006-Kharagpur], , (A) Linear, stable and invertible, , (B) Non-linear, stable and non-invertible, , (C) Linear, stable and non-invertible, , (D) Linear, unstable and invertible, , Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the inputoutput relationship,, , x[n], , y[n] = 0,, x[n + 1], , , n ≥1, n=0, n ≤ −1, , where x[n] is the input and y[n] is the output. The above system has the properties : [GATE EC 2003-Madras], , Q.15, , (A) P, S but not Q, R, , (B) P, Q, S but not R, , (C) P, Q, R, S, , (D) Q, R, S but not P, , The impulse response, , h(t ), , of a linear time-invariant continuous time system is described by, , h(t ) = exp(αt )u (t ) + exp(βt )u (−t ) , where u (t ) denotes the unit step function, and α and β are real constants. This, system is stable if :, , [GATE EC 2008-Bangalore], , (A) α is positive and β is positive, (C), Q.16, , α is positive and β is negative, , (B), , α is negative and β is negative, , (D) α is negative and β is positive, , The impulse response h[ n ] of a linear time-invariant system is given by, , h[n] = u[n + 3] + u[n − 2] − 2u[n − 7], Where u[n] is the unit step sequence. The above system is, (A) Stable but not causal, , (B) Stable and causal, , (C) Causal but unstable, , (D) Unstable and not causal, , [GATE EC 2004-Delhi], , . Common Data for Questions 17 to 19 ., The impulse response of continuous-time LTI system is given. Determine whether the system is causal and/or stable, and choose correct option., Q.17, , Q.18, , h(t ) = e −6|t |, (A) causal and stable, , (B) causal but not stable, , (C) stable but not causal, , (D) neither causal nor stable, , h(t ) = e −6 t u (3 − t ), (A) causal and stable, , (B) causal but not stable, , (C) stable but not causal, , (D) neither causal nor stable, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Signals & Systems : GATE 2021-22 [EC/EE/IN], , 8, Q.19, , GATE ACADEMY®, , h(t ) = e −4 t u (t − 2), (A) causal and stable, , (B) causal but not stable, , (C) stable but not causal, , (D) neither causal nor stable, , 3. Fourier Series, Q.1, , Let f ( x) be a real, periodic function satisfying f (− x) = − f ( x) . The general of its Fourier series representation would, be, , Q.2, , [GATE EE 2016-Bangalore], , (A), , f ( x) = a0 + k =1 ak cos (kx), , (B), , f ( x) = k =1 bk sin (kx ), , (C), , f ( x) = a0 + k =1 b2 k cos (kx), , (D), , f ( x) = k = 0 a2 k +1 sin (2k + 1) x, , ∞, , ∞, , ∞, , ∞, , A periodic variable x is shown in the figure as a function of time. The root-mean-square (rms) value of x is, ___________., , [GATE EC 2014-Kharagpur], , x, 1, t, , 0, T/2, , T/2, , ∞, , Q.3, , The Fourier series expansion f (t ) = a0 + an cos nωt + bn sin nωt, n =1, , of the periodic signal shown below will contain the following nonzero terms, , [GATE EE 2011-Madras], , f (t ), , (A) a0 and bn , n =1,3,5,...∞, (C), Q.4, , t, , 0, (B), , a0 , an and bn , n =1, 2,3,...∞, , a0 and an , n =1, 2,3,...∞, , (D) a0 and an , n = 1,3,...∞, , The trigonometric Fourier series for the waveform f(t) shown below contains, , [GATE EC 2010-Guwahati], , f (t ), , A, -T, - 3T, 4, , T /2, , -T / 2, -T, 4, , T, 4, , T, 3T, 4, , t, , - 2A, , (A) only cosine terms and zero value for the dc component., (B) only cosine terms and a positive value for the dc component., (C) only cosine terms and a negative value for the dc component., (D) only sine terms and a negative value for the dc component., ∞, , Q.5, , f ( x) , shown in the adjoining figure is represented by f ( x) = a0 + [an cos(nx) +bn sin(nx)] . The value of a0 is, n =1, , [GATE IN 2010-Guwahati], , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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Digital Electronics : GATE 2021-22 [EC/EE/IN], , 9, , (A) 0, (C), Q.6, , GATE ACADEMY®, (B), , π, , π/ 2, , (D) 2π, , x (t ) is a real valued function of a real variable with period T. Its trigonometric Fourier series expansion contains, no terms of frequency ω = 2π (2k ) / T ; k = 1, 2,.... Also, no sine terms are present. Then x(t ) satisfies the equation, [GATE EE 2006-Kharagpur], , Q.7, , (A), , x(t ) = − x(t − T ), , (B), , x(t ) = x(T − t ) = − x(−t ), , (C), , x(t ) = x(T − t ) = − x(t − T / 2), , (D), , x(t ) = x(t − T ) = x(t − T / 2), , For the triangular wave from shown in the figure, the RMS value of the voltage is equal to [GATE EE 2005-Bombay], v(t ), , 1, , T /2, , 1, 6, , (A), (C), Q.8, , T, , 1, 3, , t, , 2T, , 3T /2, , (B), , 1, 3, , (D), , 2, 3, , The rms value of the periodic waveform given in figure is, , [GATE EE 2004-Delhi], , I, 6, , T, , t, , T /2, -6, , (A) 2 6 A, (C), Q.9, , (B), , 4/3 A, , 6 2A, , (D) 1.5A, , Fourier series for the waveform, f(t) shown in figure. [GATE EE 2002-Bangalore], , (A), , 8, π2, , 1, 1, , , sin(πt) + 9 sin(3πt) + 25 sin(5πt) + ........., , , , (B), , 8, π2, , 1, 1, , , sin(πt) − 9 cos(3πt) + 25 sin(5πt) + ........., , , , (C), , 8, π2, , 1, 1, , , cos( πt) + 9 cos(3πt) + 25 cos(5πt) + ........., , , , (D), , 8, π2, , 1, 1, , , cos(πt) − 9 sin(3πt) + 25 sin(5πt) + ........., , , , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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10, Q.10, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , The Fourier series expansion of a real periodic signal with fundamental frequency f0 is given by, , g p (t ) =, , ∞, , C, , n, , n =−∞, , exp( j 2πnf 0t ) . It is given that C3 = 3 + j 5 then C−3 is, , (A) 5 + j3, , (B) –3 – j5, , (C) – 5 + j3, , (D) 3 – j5, , [GATE EC 2003-Madras], , . Statement for Linked Questions 11 to 18 ., Consider a continuous time periodic signal x(t ) with fundamental period T and Fourier series coefficients cn ., Q.11, , The Fourier series coefficient of the signal y (t ) = x(t − t0 ) + x(t + t0 ) is, , 2π , (A) 2cos nt0 cn, T, , (C), Q.12, , Q.13, , Q.14, , e−t0 cn + et0 c− n, , (B), , −t, t, (D) e 0 c− n + e 0 cn, , The Fourier series coefficient of the even part of x(t ) i.e. y (t ) = xe (t ) is, (A), , cn + c− n, 2, , (B), , cn − c− n, 2, , (C), , cn + c−* n, 2, , (D), , cn − c−* n, 2, , The Fourier series coefficient of the signal y (t ) = Re{x(t )} is, (A), , cn + c− n, 2, , (B), , cn − c− n, 2, , (C), , cn + c−* n, 2, , (D), , cn − c−* n, 2, , The Fourier series coefficient of the signal y (t ) =, , d 2 x (t ), is, dt 2, , 2, , 2πn , (A) , cn, T , 2, , (C), Q.15, , 2πn , j, cn, T , , (C), , Q.17, , 2, , (B), , 2πn , −, cn, T , 2, , 2πn , (D) − j , cn, T , , The Fourier series coefficient of the signal y (t ) = x(4 − t ) is, − jω 4 n, (A) c−ne 0, , Q.16, , 2π , 2sin nt0 cn, T, , , c− n e jω0 4 n, , (B), , cn e jω0 4 n, , − jω 4 n, (D) cn e 0, , The Fourier series coefficient of the signal y (t ) = x(t ) ⊗ x(t ) is, (A) cn2, , (B), , (C) T ⋅ cn2, , (D) 2cn, , c− n, , The Fourier series coefficient of the signal y (t ) = x(4t − 1) is, (A), , 8π, cn, T, , (C), , e, , 8π , − jn , T , , (B), , cn, , 4π, cn, T, , (D) e, , 2π , − jn , T , , cn, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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12, Q.21, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , cos 4 t, 3, 1, 1, (A) C0 = , C2 = C−2 = , C4 = C−4 =, 8, 4, 16, , (C), , 3, 1, 1, C0 = , C2 = C−2 = , C4 = C−4 =, 8, 4, 8, , (B), , 3, 1, 1, C0 = , C1 = C−1 = , C2 = C−2 =, 8, 4, 16, , 3, 1, 1, (D) C0 = , C1 = C−1 = , C2 = C−2 =, 8, 4, 8, , 4. Fourier Transform, Q.1, , The signal x (t ) is described by, , for − 1 ≤ t ≤ +1, , 1, x(t ) = , 0, , otherwise, , Two of the angular frequencies at which its Fourier transform becomes zero are : [GATE EC 2008-Bangalore], (A) π, 2π, (C), Q.2, , Let, , 0, π, , (D) 2π, 2.5π, , 1, x(t ) = rect t − , 2, , sinc( x) =, , rect( x) = 1, , (where, , Q.3, , for, , −, , 1, 1, ≤x≤, 2, 2, , and, , sin πx, , the Fourier Transform of x(t ) + x( −t ) will be given by :, πx, , ω, (A) sinc , 2π , , (C), , 0.5π, 1.5π, , (B), , (B), , ω, ω, 2sinc cos , 2π , 2, , otherwise)., , Then, , if, , [GATE EE 2008-Bangalore], , ω, 2sinc , , 2π , , ω ω, (D) sinc sin , 2π 2 , , FT, X ( jω) be the Fourier transform pair. The Fourier transform of the signal x (5t − 3) in terms of X ( jω), Let x(t ) ←⎯→, , is given as, , Q.4, , zero, , − j 3ω, 5, , [GATE EC 2006-Kharagpur], j 3ω, 5, , jω , X, , 5 , , (A), , 1, e, 5, , jω , X, , 5 , , (B), , 1, e, 5, , (C), , 1 − j 3ω jω , e, X, , 5, 5 , , (D), , 1 j 3ω jω , e X, , 5, 5 , , The magnitude of Fourier transform X (ω) of a function x( t ) is shown below in figure (a). The magnitude of Fourier, transform Y (ω) of another function y ( t ) is shown in figure (b). The phases of X (ω) and Y (ω) are zero for all ω ., The magnitude and frequency units are identical in both the figure. The function y ( t ) can be expressed in terms, of x( t ) as, , [GATE IN 2006-Kharagpur], X (w), , Y (w), , 3, , 1, , -100, , Fig. (a), , 100, , w, , - 50, , (A), , 2 t, x , 3 2, , (B), , 3, x(2t ), 2, , (C), , 2, x(2t ), 3, , (D), , 3 t, x , 2 2, , Fig. (b), , 50, , w, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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14, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , Which of the following corresponds to Fourier transform of signal, , 1, , (A), , (B), 4p, , 0, , 2p, , 1, , w, , -1, , (D), , 1 / 4p, , 2p, , 0, , 4p, , 2p, , w, , 0, , 2p, , If x(t ) = u (−2 − t ) + u (t − 2), then what will be the Fourier transform of, (A) 2 cos 2ω, (C), , w, , 4p, , 4p, , 1 / 2p, , Q.12, , 2p, , 0, , (C), , Q.11, , dx (t ), ?, dt, , 2π [ δ(ω + 2) + δ(ω − 2)], , (B), , −2 j sin 2ω, , (D), , 1, 1, +, 2 + jω 2 − jω, , The Fourier transform of signal h(t ) is H ( j ω) = 2 cos ω., , w, , 4p, dx(t ), ?, dt, , sin 2ω, . The value of h(0) is, ω, , [GATE EC, EE, IN 2012-Delhi], (A) 1 / 4, , (B), , 1/ 2, , (C) 1, , (D) 2, . Common Data for Questions 13 & 14 ., , Consider the signal X ( jω) shown below whose inverse Fourier transform is x (t ) ., X ( jw), , 2, , -5, , -3, , -1, , 0, , 1, , 3, , w, , ∞, , Q.13, , The value of, , x(t ) dt, , is, , −∞, , Q.14, , Q.15, , 2π, , (A) 1, , (B), , (C) 1 / 2π, , (D) ∞, , The value of x(0) is, (A) 0, , (B), , 8, , (C) 4, , (D) 4 / π, , |f |, | f |≤B, 1 −, If F [ x(t ) ] = X ( f ) = , B, 0, elsewhere, , Then value of x(0) is, (A) 1, , (B) B, , (C) 1 / 2, , (D) B / 2, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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15, Q.16, , Digital Electronics : GATE 2021-22 [EC/EE/IN], 1, A signal is represented by x(t ) = , 0, , GATE ACADEMY®, , t <1, t >1, , The Fourier transform of the convolved signal y (t ) = x(2t ) * x(t / 2) is, [GATE EE 2014-Kharagpur], , Q.17, , (A), , 4, ω, sin sin(2ω), ω2, 2, , (B), , 4, ω, sin , ω2, 2, , (C), , 4, sin(2ω), ω2, , (D), , 4, sin 2 ω, ω2, , A linear time invariant causal system has a frequency response given in polar form as, , x(t ) = sin t , the output is, (A), (C), Q.18, , 1, 2, 1, 2, , 1, 2, , 1+ ω, , ∠ − tan −1 ω . For input, , [GATE IN 2009-Roorkee], , cos t, , (B), , sin t, , (D), , π, cos t − , 2, 4, , 1, , π, sin t − , 2, 4, , 1, , sin(πx) , , is the input to a Linear Time Invariant system, A signal x(t ) = sinc(αt ) where α is a real constant sinc( x) =, πx , , , whose impulse response h(t ) = sin c(βt ) where β is a real constant. If min(α, β) denotes the minimum of α and β, and similarly max(α, β) denotes the maximum of α and β , and K is a constant, which one of the following, statements is true about the output of the system?, , [GATE EE 2008-Bangalore], , (A) It will be of the form Ksinc( γt ) where γ = min(α, β), (B) It will be of the form Ksinc( γt ) where γ = max(α, β), (C) It will be of the form K sin c(αt ), (D) It cannot be a sinc type of signal, Q.19, , Let a signal a1 sin(ω1t + φ1 ) be applied to a stable linear time invariant system. Let the corresponding steady state, output be represented as a2 F (ω2 t + φ2 ). Then which of the following statements is true?, [GATE EE 2007-Kanpur], (A) F is not necessarily a ‘sine’ or ‘cosine’ function but must be periodic with ω1 = ω2, (B) F must be a ‘sine’ or ‘cosine’ function with a1 = a 2, (C) F must be a ‘sine’ function with ω1 = ω2 and φ1 = φ2, (D) F must be a ‘sine’ or ‘cosine’ function with ω1 = ω2, , Q.20, , A causal LTI filter has the frequency response H ( jω) shown below. For the input signal x (t ) = e − jt , output will be, H ( jw), j2, , -1, , 0, , 1, , w, , - j2, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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17, Q.25, , Q.26, , Digital Electronics : GATE 2021-22 [EC/EE/IN], A signal is given by x(t ) =, , GATE ACADEMY®, , 3, d, t, t, rect ⊗ rect . If y (t ) = x (t ) , then energy of y (t ) is, 2, dt, 8, 2, , (A) 9, , (B) 18, , (C) 36, , (D) None of these, , The energy of the signal, , sin at, is, πt, a/π, , (C), , 2a, , (B), , (C), , aπ, , (D) 1 / aπ, , 5. Laplace Transform, Q.1, , Q.2, , Q.3, , The Laplace Transform of f (t ) = e 2 t sin(5t ) u (t ) is, , [GATE EE 2016-Bangalore], , (A), , 5, s − 4s + 29, , (B), , 5, s +5, , (C), , s−2, s − 4s + 29, , (D), , 5, s+5, , 2, , 2, , 2, , 1 if a ≤ t ≤ b, is, The bilateral Laplace transform of a function f (t ) = , 0 otherwise, (A), , a −b, s, , (B), , e z ( a − b), s, , (C), , e − as − e − bs, s, , (D), , e− ( a −b ), s, , [GATE EC 2015-Kharagpur], , Let x(t ) = αβ s(t ) + βs (−t ) with s (t ) = e −4t u (t ) where u (t ) is unit step function. If the bilateral Laplace transform of, , x(t ) is, , [GATE EC 2015-Kharagpur], , X ( s) =, , 16, s 2 − 16, , − 4 < Re{s} < 4, , Then the value of β is _______., Q.4, , Consider the function g (t ) = e − t sin(2 πt )u (t ) where u (t ) is the unit step function. The area under g (t ) is ______., [GATE EC 2015-Kanpur], , Q.5, , The Laplace transform of f (t ) = 2, , 3, −, t, is s 2 . The Laplace transform of g (t ) =, π, , 1, is, πt, [GATE EE 2015-Kharagpur], , 5, −, 2, , (A), , 3s, 2, , (C), , s2, , s, , (D), , s2, , 1, , Q.6, , −, , (B), , 1, 2, , 3, , The unilateral Laplace transform of f (t ) is, , 1, Which one of the following is the unilateral Laplace transform, s + s +1, 2, , of g (t ) = t. f (t ) ?, (A), (C), , −s, ( s + s + 1)2, 2, , s, ( s 2 + s + 1)2, , [GATE EC 2014-Kharagpur], (B), , −(2s + 1), ( s 2 + s + 1)2, , (D), , 2s + 1, ( s 2 + s + 1)2, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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18, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , Which of the following plot represents correct ROC of a signal x(t ) = e2t u (−t ) − e−5t u (t ) ?, Im( s ), , Im( s ), , 5, , Re( s ), , +, , +, , –2, , –5, , +, , (B), , +, , (A), , Re( s ), , +, , Q.7, , Re( s ), , 2, , Im( s ), , Im( s ), , (D), , –5, , 2, , Re( s ), , +, , +, , +, , (C), , –5, , 2, , Let X ( s) be the Laplace transform of signal x(t ) shown in figure (A) given as, , Q.8, , X (s) =, , 1, 1 − 3e−2 s + 2e−3s , s2 , , x(t ), , 2, t, , 0, 3, 2, The Laplace transform of y (t ) shown in figure (B) will be, y (t ), , 2, , –3, , –2, , 0, , t, , (A), , 1, 1 + 3e −2 s − 2e −3 s , 2 , s, , (B), , −1, 1 − 3e −2 s + 2e −3 s , 2 , s, , (C), , 1, 1 − 3e 2 s + 2e3 s , s2 , , (D), , −1, −1 + 3e −2 s + 2e −3 s , s2 , , The Laplace transform and its ROC of a signal x(t ) = 3e − t u (t ) + 2et u (−t ) is, , Q.9, , Q.10, , (A), , s −5, , ROC : −1 < Re ( s ) < 1, ( s 2 − 1), , (B), , 5, , ROC : −1 < Re ( s) < 1, ( s + 1), , (C), , 5s + 1, , ROC : Re ( s ) < 1, ( s 2 − 1), , (D), , s −5, , ROC : Re ( s ) > −1, ( s 2 + 1), , The Laplace transform of a signal x(t ) is X ( s ) =, , d2 1 , , ,, ds 2 s − 3 , , ROC : Re( s ) > 3, , The signal x(t ) is, (A) t 2 e3t u (t ), (C), , t 2 u (t − 3), , (B), , −t 2 e3t u (t ), , (D) (t − 3)2 u (t − 3), , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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19, Q.11, , Q.12, , Digital Electronics : GATE 2021-22 [EC/EE/IN], The Laplace transform of et, 1− s, , Re( s ) < −1, s +1, , (B), , 1− s, , Re( s ) > −1, s +1, , (C), , s −1, , Re( s ) < −1, s +1, , (D), , s −1, , Re( s ) > −1, s +1, , Determine the Laplace Transform of the signal t., , (C), , Q.14, , d −2 t, e u (−t ) is, dt , , (A), , (A) −, , Q.13, , GATE ACADEMY®, , [ s 2 + 4s + 2], [ s 2 + 2s + 2]2, , (B), , s 2 + 2s + 2, [ s 2 + 4s + 2]2, , If F (s) = L [ f (t )] =, , d −t, e cos t.u (t ) , dt , , s 2 + 4s + 2, [ s 2 + 2s + 2]2, , (D) −, , [ s 2 + 2s + 2], [ s 2 + 4s + 2]2, , 2(s + 1), then the initial and final values of f (t ) are respectively [GATE EC 2011-Madras], s + 4s + 7, 2, , (A) 0, 2, , (B) 2, 0, , (C) 0, 2 / 7, , (D) 2 / 7, 0, , , 3s + 1, −1 , Given f (t ) = L 3, ., 2, s + 4s + ( K − 3) s , If lim f (t ) = 1 , then the value of K is, t →∞, , [GATE EC 2010-Guwahati], , Q.15, , (A) 1, , (B) 2, , (C) 3, , (D) 4, , If L[ f (t )] =, , 2( s + 1), , then f (0 + ) and f (∞) respectively are given by, s 2 + 2s + 5, , (A) 0, 2, , (B) 2, 0, , (C) 0, 1, , (D), , [GATE EC 1995-Kanpur], , 2, ,0, 5, , . Common Data for Questions 16 to 18 ., Let X ( s) =, Q.16, , 2s + 4, , the inverse LT of X ( s) for, s 2 + 4s + 3, , ROC : Re ( s ) > −1, −t, −3t, (A) − e + e u(−t ), , (C), Q.17, , − e − t u ( − t ) + e − 3 t u (t ), , e−t + e−3t u(t ), , (D) e − t u (t ) − e −3t u (−t ), , ROC : Re ( s ) < −3, −t, −3t, (A) − e + e u(−t ), , (C), Q.18, , (B), , − e − t u ( − t ) + e − 3 t u (t ), , (B), , e−t + e−3t u(t ), , (D) e − t u (t ) − e −3t u (−t ), , ROC : −3 < Re ( s ) < −1, −t, −3t, (A) − e + e u(−t ), , (C), , − e − t u ( − t ) + e − 3 t u (t ), , (B), , e−t + e−3t u(t ), , (D) e − t u (t ) − e −3t u (−t ), , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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20, Q.19, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , Consider a causal LTI system characterized by differential equation, −, , dy(t ) 1, + y(t ) = 3x(t ) . The response of the system, dt, 6, , t, , to the input x(t ) = 3e 3 u (t ) , where u (t ) denotes the unit step function, is, −, , t, , −, , t, , (A) 9e 3 u (t ), (C), Q.20, , (B), −, , −, , t, , 9e 6 u (t ), , t, , −, , 9e 3 u (t ) − 6e 6 u (t ), , [GATE EE 2016-Bangalore], , t, , −, , t, , (D) 54e 6 u (t ) − 54e 3 u (t ), , Input x(t ) and output y (t ) of an LTI system are related by the differential equation y "(t ) − y '(t ) − 6 y (t ) = x(t ) . If the, system is neither causal nor stable, the impulse response h(t ) of the system is, (A), , 1 3t, 1, e u(−t ) + e−2t u(−t ), 5, 5, , (B), , (C), , 1 3t, 1, e u(−t ) − e−2t u (t ), 5, 5, , 1 3t, 1 −2t, (D) − e u(−t ) − e u(t ), 5, 5, , [GATE EC 2015-Kharagpur], , 1, 1, − e3t u (−t ) + e−2t u (−t ), 5, 5, , . Statement for Linked Questions 21 & 22 ., A continuous LTI system with an input x(t ) and output y (t ) is described by following differential equation, , d 2 y(t ) dy(t ), −, − 2 y(t ) = x(t ), dt 2, dt, Q.21, , Q.22, , Q.23, , If the system is stable, the impulse response h(t) of the system will be, (A), , 1 2t, 1, e u (t ) − e − t u (t ), 3, 3, , (B), , 1, 1, − e 2t u (−t ) + e − t u ( −t ), 3, 3, , (C), , 1, 1, − e2t u (−t ) − e−t u (t ), 3, 3, , (D), , 1 2t, 1, e u (t ) + e − t u (t ), 3, 3, , If the system is causal, the impulse response h(t ) of the system will be, (A), , 1, 1, − e 2t u (−t ) + e − t u ( −t ), 3, 3, , (B), , 1, 1, − e −2t u (−t ) − e −t u (t ), 3, 3, , (C), , 1 2t, 1, e u (t ) + e − t u (t ), 3, 3, , (D), , 1 2t, 1, e u (t ) − e − t u (t ), 3, 3, , The transfer function of a system is, , Y (s), s, =, . The steady state output y (t ) is A cos(2t + φ) for the input cos (2t ), R( s) s + 2, , . The values of A and φ , respectively are, (A), (C), Q.24, , 1, , [GATE EE 2016-Bangalore], , , − 450, , (B), , 2, − 450, , (D), , 2, , 1, 2, , , + 450, , 2, + 450, , Consider a linear time-invariant system with transfer function [GATE EE 2016-Bangalore], , H ( s) =, , 1, ( s + 1), , If the input is cos(t ) and the steady state output is A cos(t + α) , then the value of A is _________., Q.25, , In the system shown below, x(t ) = sin t.u(t ) . In the steady state, the response y(t ) will be, , x(t ), , 1, s +1, , y (t ), [GATE EC 2006-Kharagpur], , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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21, , Digital Electronics : GATE 2021-22 [EC/EE/IN], (A), (C), , Q.26, , 1, 2, 1, 2, , GATE ACADEMY®, , π, sin t − , 4, , (B), , e−t sin(t ), , (D) sin(t ) − cos(t ), , 1, 2, , π, sin t + , 4, , The output of a continuous-time, linear time-invariant system is denoted by T {x(t )} where x(t ) is the input signal., A signal z (t ) is called eigen-signal of the system T , when T {z (t )} = γ z (t ) , where γ is a complex number, in general,, and is called an eigenvalue of T. Suppose the impulse response of the system T is real and even. Which of the, following statements is TRUE?, , [GATE EE 2016-Bangalore], , (A) cos (t ) is an eigen-signal but sin (t ) is not, (B) cos (t ) and sin (t ) are both eigen-signals but with different eigenvalues, (C) sin (t ) is an eigen-signal but cos (t ) is not, (D) cos (t ) and sin (t ) are both eigen-signals with identical eigenvalues, , 6. Z - Transform, Q.1, , Consider the sequence x [ n ] = a n u [ n ] + b n u [ n ] , where u [ n ] denotes the unit-step sequence and 0 < a < b < 1 . The, region of convergence (ROC) of the z-transform of x [ n ] is, , Q.2, , (A), , z > a, , (B), , z > b, , (C), , z < a, , (D), , a < z < b, , [GATE EC 2016-Bangalore], , The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region, in in the z-plane. If the signal x[ n] = (2.0) n , − ∞ < n < +∞ , then the ROC of its z-transform is represented by, [GATE EC 2016-Bangalore], (A), , (B), , Im, Unit circle, , (C), , Unit circle, , z-plane, , 0.5, , 2, , Im, , Re, , 0.5, , Unit circle, Unit circle, , Re, , 2, , Im, , (D), , Im, , z-plane, , z-plane, , z-plane, , 0.5, , 2, , Re, , 0.5, , 2, , Re, , (ROC does not exist), , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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22, , Signals & Systems : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , The signal x[ n] shown in the figure below is convolved with itself to get y[ n] . The value of y[−1] is _____., , Q.3, , [GATE IN 2016-Bangalore], 1, , 1, x[n], 1, , -1, , 0, , n, , 2, -1, , ∞, , Q.4, , The value of, , 1, , n 2 , , n, , is ______., , n =0, , [GATE EC 2015-Kanpur], n, , Two causal discrete-time signals x[ n] and y[ n ] are related as y[n] =, , Q.5, , x[m] . If the z-transform of, , m=0, , the value of x[2] is _________., , y[ n ] is, , 2, ,, z ( z − 1)2, , [GATE EC 2015-Kanpur], , Suppose x [ n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles, , Q.6, , and two zeroes. The poles are at z = ±2 j. Which one of the following statements is TRUE for the single x [ n] ?, [GATE EC 2015-Kanpur], (A) It is a finite duration signal, , (B) It is a causal signal, , (C) It is a non-causal signal, , (D) It is a periodic signal, , 1, Consider the difference equations y[n] − y[n − 1] = x[n] and suppose that x[n] =, 3, , Q.7, , of initial rest, the solution of y[n], n ≥ 0 is, n, , 1, 1, (A) 3 − 2 , 3, 2, n, , (C), , [GATE IN 2011-Madras], , n, , 1 11, 2 + , 3 3 2, , n, , 1, u[ n] . Assuming the conditions, 2, , n, , (B), , 1, 1, −2 + 3 , 3, 2, , (D), , 11 2 1, + , 33 3 2, , n, , n, , n, , n, , A discrete time linear shift-invariant system has an impulse response h[ n] with h[0] = 1 , h[1] = −1, h[2] = 2, and zero, , Q.8, , otherwise. The system is given an input sequence x[ n ] with x[0] = x[2] = 1 , and zero otherwise. The number of, nonzero samples in the output sequence y[ n ] , and the value of y[2] are, respectively, [GATE EC 2008-Bangalore], (A) 5, 2, , (B) 6, 2, , (C) 6, 1, , (D) 5, 3, , The Z-Transform X ( z ) of a sequence x[n] is given by X ( z) =, , Q.9, , 0.5, 1 − 2 z −1, , X ( z ) includes the unit circle. The value of x[0] is, (A) − 0.5, If X ( z ) = e, , [GATE EC 2007-Kanpur], , (B) 0, , (C) 0.25, Q.10, , . It is given that the region of convergence of, , (D) 0.5, a/ z, , for | z | > 0 then x[n] is, , (A), , an, u[n], n!, , (B), , n!an u[n], , (C), , ( n + 1)! a n u[ n], , (D), , 1, a n u[n], (n + 1)!, , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
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23, , Digital Electronics : GATE 2021-22 [EC/EE/IN], , GATE ACADEMY®, , . Common Data for Questions 11 to 14 ., z, , ZT, , If x[ n] ←⎯⎯, → X ( z ) and X ( z ) =, Q.11, , (C), , (C), , z/2, ( z / 2) + 2, z/2, , (D), , 2, , ( z / 2) + 4, , 2z, 2, , z +4, 2z, 2, , z +8, , z3 − 4 z, , (B), , 2, , z +4, z3 + 4 z, , (D), , z2 + 4, , z3 − 4 z, ( z 2 + 4) 2, z3 + 4z, ( z 2 + 4) 2, , y[n] = x[n + 1] + x[n − 1], , (C), , ( z 2 + 1), , z, 2, , z +4, z, , (B), , (D) (1 + z −2 ), , 2, , z +4, , z, , ( z + z −1 ), , 2, , z +4, z, 2, , z +4, , y[n] = [n − 3]x[n − 2], (A), , (C), Q.15, , (B), , 2, , (A) ( z − z −1 ), , Q.14, , ; | z | < 2 then find Y ( z ) for following y[n], , y[n] = nx[n], (A), , Q.13, , z +4, , y[n] = 2n x[n], (A), , Q.12, , 2, , 8 z −1, ( z 2 + 4) 2, 4 z −1, ( z 2 + 4) 2, , (B), , (D), , − 4 z −1, ( z 2 + 4) 2, − 8 z −1, ( z 2 + 4) 2, , If X ( z ) = 2 + 3 z −1 + 4 z −2 then initial & final values of x[n] are, (A) 1, 0, , (B) 2, 0, , (C) 2, 9, , (D) 0, 2, , , , Telegram Channel :, , GATE ACADEMY : https://www.youtube.com/channel/UCnaOzPCUym-vNapCjV2p9Pg, , Online Test Series, , Gate academy official, , Live class room: https://play.google.com/store/apps/details?id=com.gateacademy1, , http://onlinetestseries.gateacademy.co.in
