GATE Networks, Signals and Systems: Continuous-time Signals – Previous Year Questions
28 GATE previous year questions on Continuous-time Signals (Networks, Signals and Systems, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q18 – A periodic signal x(t) has a trigonometric Fourier series expansion x(t) = a 0 + n=1(a n n 0 t + b n n 0 t) If x(t) = -x(-t) = -x(t - / 0), we can…
- GATE 2017 EC Q41 – Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let \a k\ be the complex Fourier series coefficients of x(t),…
- GATE 2015 EC Q27 – The result of the convolution x(-t) * (-t - t 0) is
- GATE 2015 EC Q28 – The waveform of a periodic signal x(t) is shown in the figure. [Figure: A periodic sawtooth. In each period of 3 s the signal starts at 3 and falls…
- GATE 2016 EC Q20 – A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed…
- GATE 2016 EC Q40 – The Laplace transform of the causal periodic square wave of period T shown in the figure below is
- GATE 2018 EC Q24 – Let x(t) be a periodic function with period T=10. The Fourier series coefficients for this series are denoted by a k, that is, x(t)= k=-a kejk2Tt The…
- GATE 2018 EC Q64 – A band limited low-pass signal x(t) of bandwidth 5 kHz is sampled at a sampling rate f s. The signal x(t) is reconstructed using the reconstruction…
- GATE 2019 EC Q16 – For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N p and the number of system zeros N z…
- GATE 2019 EC Q31 – Consider the signal f(t)=1+2( t)+3(23t)+4(2t+4), where t is in seconds. Its fundamental time period, in seconds, is .
- GATE 2020 EC Q62 – X() is the Fourier transform of x(t) shown below. The value of - X() 2\,d (rounded off to two decimal places) is .
- GATE 2021 EC Q14 – Consider a real-valued base-band signal x(t), band limited to 10 kHz. The Nyquist rate for the signal y(t)=x(t)\,x(1+ t2) is
- GATE 2021 EC Q49 – The exponential Fourier series representation of a continuous-time periodic signal x(t) is defined as x(t)= k=-a kejk 0t where 0 is the fundamental…
- GATE 2022 EC Q15 – The Fourier transform X(j) of the signal x(t)=t(1+t2)2 is .
- GATE 2022 EC Q33 – Let x 1(t)=e-tu(t) and x 2(t)=u(t)-u(t-2), where u() denotes the unit step function. If y(t) denotes the convolution of x 1(t) and x 2(t), then ty(t)=…
- GATE 2023 EC Q28 – The Fourier transform X() of x(t)=e-t2 is Note: -e-y2dy=
- GATE 2023 EC Q29 – In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a)…
- GATE 2023 EC Q49 – Let x(t)=10(10.5Wt) be passed through an LTI system having impulse response h(t)=( Wt t)210Wt. The output of the system is
- GATE 2024 EC Q44 – Consider two continuous time signals x(t) and y(t) as shown below. If X(f) denotes the Fourier transform of x(t), then the Fourier transform of y(t)…
- GATE 2024 EC Q48 – A continuous time signal x(t)=2(8 t+/3) is sampled at a rate of 15 Hz. The sampled signal x s(t) when passed through an LTI system with impulse…
- GATE 2025 EC Q18 – Consider a continuous-time, real-valued signal f(t) whose Fourier transform F()= -f(t)(-j t)\,dt exists. Which one of the following statements is…
- GATE 2025 EC Q38 – Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [- c, c], where c is in rad/sec.…
- GATE 2025 EC Q55 – Let f(t) be a periodic signal with fundamental period T 0>0. Consider the signal y(t)=f( t), where >1. The Fourier series expansions of f(t) and y(t)…
- GATE 2026 EC Q15 – Two analog signals x 1(t) and x 2(t) (t in second), are sampled at a rate F s = 40 Hz, where x 1(t)=(20 t),\, t0, and x 2(t)=(100 t),\, t0. The first…
- GATE 2026 EC Q37 – The continuous time signal x(t) is real, periodic with period T and satisfies the Dirichlet conditions. The Fourier series representation of x(t)= -a…
- GATE 2026 EC Q43 – Consider a real signal x(t), -<t<, such that x(t)=0 for t<0, x(t)=2 for 0 t<1 and x(t)=0 for t1. Let E[x(t)]= -[x(t)]2dt. Which of the following…
- GATE 2026 EC Q46 – Consider a real baseband signal x(t)=e-2t, for t (in seconds) 0. If 99% of energy of x(t) lies within B Hz, then which of the following options is…
- GATE 2026 EC Q58 – Let x 1(t)=(2 nt) and x 2(t)=2(4 nt) represent two sinusoids for a positive integer n and -<t<. Which of the following statements about x 1(t) and x…