GATE Networks, Signals and Systems: Discrete-time Signals – Previous Year Questions
25 GATE previous year questions on Discrete-time Signals (Networks, Signals and Systems, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q42 – Two discrete-time signals x[n] and h[n] are both non-zero only for n = 0, 1, 2, and are zero otherwise. It is given that x[0] = 1, x[1] = 2, x[2] = 1,…
- GATE 2017 EC Q43 – Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by h[0] = 13; h[1] = 13; h[2] =…
- GATE 2015 EC Q53 – Two sequences [a, b, c] and [A, B, C] are related as, bmatrix A \\ B \\ C bmatrix = bmatrix 1 & 1 & 1 \\ 1 & W 3-1 & W 3-2 \\ 1 & W 3-2 & W 3-4…
- GATE 2015 EC Q54 – For the discrete-time system shown in the figure, the poles of the system transfer function are located at
- GATE 2015 EC Q55 – The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse…
- GATE 2016 EC Q17 – A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period T s. In which one of the following…
- GATE 2016 EC Q18 – Consider the sequence x[n] = an u[n] + bn u[n], where u[n] denotes the unit-step sequence and 0 < a < b < 1. The region of convergence (ROC) of the…
- GATE 2016 EC Q45 – Consider the signal x[n] = 6[n+2] + 3[n+1] + 8[n] + 7[n-1] + 4[n-2]. If X(ej) is the discrete-time Fourier transform of x[n], then 1 - X(ej)2(2) \, d…
- GATE 2018 EC Q23 – A discrete-time all-pass system has two of its poles at 0.250 and 230. Which one of the following statements about the system is TRUE?
- GATE 2018 EC Q65 – Let X[k]=k+1, 0 k7 be 8-point DFT of a sequence x[n], where X[k]= n=0N-1x[n]e-j2 nk/N. The value (correct to two decimal places) of n=03x[2n] is .
- GATE 2019 EC Q13 – Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z)=H(z)H(1z) has a zero at z=12+12j, and P(z) has a total of four zeros,…
- GATE 2019 EC Q38 – Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the…
- GATE 2019 EC Q39 – It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form x[n]=c 1(-j n2)+c 2(j n2), where c 1 and…
- GATE 2019 EC Q54 – Let h[n] be a length-7 discrete-time finite impulse response filter, given by h[0]=4,\ h[1]=3,\ h[2]=2,\ h[3]=1,\ h[-1]=-3,\ h[-2]=-2,\ h[-3]=-1, and…
- GATE 2020 EC Q24 – Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation…
- GATE 2020 EC Q39 – A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t)=(200 t) at sampling instants t=n/400, n=0,1,,7.…
- GATE 2020 EC Q63 – The transfer function of a stable discrete-time LTI system is H(z)=K(z-)z+0.5, where K and are real numbers. The value of (rounded off to one decimal…
- GATE 2021 EC Q15 – Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse…
- GATE 2021 EC Q51 – Consider the signals x[n]=2n-1u[-n+2] and y[n]=2-n+2u[n+1], where u[n] is the unit step sequence. Let X(ej) and Y(ej) be the discrete-time Fourier…
- GATE 2022 EC Q55 – For a vector x=[x[0],x[1],,x[7]], the 8-point discrete Fourier transform (DFT) is denoted by X=DFT( x)=[X[0],X[1],,X[7]], where X[k]=…
- GATE 2023 EC Q47 – Consider a discrete-time periodic signal with period N=5. Let the discrete-time Fourier series (DTFS) representation be x[n]= k=04a kej2 kn5, where a…
- GATE 2023 EC Q48 – Let an input x[n] having discrete time Fourier transform X(ej)=1-e-j+2e-3j be passed through an LTI system. The frequency response of the LTI system…
- GATE 2024 EC Q56 – The radian frequency value(s) for which the discrete time sinusoidal signal x[n]=A( n+/3) has a period of 40 is/are .
- GATE 2024 EC Q59 – The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as X[k]= F\x[n]\. Another…
- GATE 2025 EC Q27 – Let x[n] be a discrete-time signal whose z-transform is X(z). Which of the following statements is/are TRUE?