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GATE EC Continuous-time Signals questions

Practise Continuous-time Signals questions for GATE EC. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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20 on this page
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Two analog signals x1(t)x_{1}(t) and x2(t)(tx_{2}(t)(t in second )), are sampled at a rate Fs=40 HzF_{s}=40 \mathrm{~Hz}, where x1(t)=cos⁡(20πt),t≥0, and x2(t)=cos⁡(100πt),t≥0x_{1}(t)=\cos (20 \pi t), t \geq 0, \text{ and } x_{2}(t)=\cos (100 \pi t), t \geq 0 The first ten samples (starting from t=0t=0 ) are considered for the analysis. Which of the following statements is TRUE?
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
The continuous time signal x(t)x(t) is real, periodic with period TT and satisfies the Dirichlet conditions. The Fourier series representation of x(t)=∑−∞∞anej(2πntT)x(t)=\sum_{-\infty}^{\infty} a_{n} e^{j\left(\frac{2 \pi n t}{T}\right)} and x(t)x(t) satisfies the following: x(t−T2)=−x(t)x\left(t-\frac{T}{2}\right)=-x(t). For any integer mm, which of the following options is …
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider a real signal x(t),−∞<t<∞x(t),-\infty < t < \infty, such that x(t)=0fort<0,x(t)=2for0≤t<1andx(t)=0fort≥1x(t) = 0\quad\text{for}\quad t <0, x(t) =2 \quad\text{for} \quad0 \leq t < 1\quad \text{and}\quad x(t) = 0\quad \text{for} \quad t \geq 1. Let E[x(t)]=∫−∞∞[x(t)]2dtE[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2} d t. Which of the following options correctly represents the ratio, …
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider a real baseband signal x(t)=e−2tx(t)=e^{-2 t}, for tt (in seconds) ≥0\geq 0. If 99%99 \% of energy of x(t)x(t) lies within B HzB \mathrm{~Hz}, then which of the following options is TRUE for the value of B?{B}?
Official PYQ2026Networks, Signals and SystemsContinuous-time SignalsMSQ · 2 marks
Let x1(t)=cos⁡(2πnt)x_{1}(t)=\cos (2 \pi n t) and x2(t)=2sin⁡(4πnt)x_{2}(t)=2 \sin (4 \pi n t) represent two sinusoids for a positive integer nn and −∞<t<∞-\infty < t < \infty. Which of the following statements about x1(t)x_{1}(t) and x2(t)x_{2}(t) is/are valid?
Official PYQ2025Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Consider a continuous-time, real-valued signal f(t)f(t) whose Fourier transform F(ω)=∫−∞∞f(t)exp⁡(−j ωt)dtF(\omega)=\int_{-\infty}^{\infty} f(t) \exp (-j \: \omega t) d t exists. Which one of the following statements is always TRUE?
Official PYQ2025Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider a continuous-time finite-energy signal f(t)f(t) whose Fourier transform vanishes outside the frequency interval [−ωc,ωc]\left[-\omega_{c}, \omega_{c}\right], where ωc\omega_{c} is in rad\mathrm{rad} / sec\mathrm{sec}. The signal f(t)f(t) is uniformly sampled to obtain y(t)=f(t) p(t)y(t)=f(t) \: p(t). Here, …
Official PYQ2025Networks, Signals and SystemsContinuous-time SignalsMSQ · 2 marks
Let f(t)f(t) be a periodic signal with fundamental period T0>0T_{0}>0. Consider the signal y(t)=f(αt)y(t)=f(\alpha t), where α>1\alpha>1. The Fourier series expansions of f(t)f(t) and y(t)y(t) are given by …
Official PYQ2024Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Consider two continuous time signals x(t)x(t) and y(t)y(t) as shown below If X(f)X(f) denotes the Fourier transform of x(t)x(t), then the Fourier transform of y(t)y(t) is ______\_\_\_\_\_\_.
Official PYQ2024Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
​​​​A continuous time signal x(t)=2cos⁡(8πt+π/3)x(t)=2 \cos (8 \pi t+\pi / 3) is sampled at a rate of 15 Hz15 \mathrm{~Hz}. The sampled signal xs(t)x_{s}(t) when passed through an LTI system with impulse response h(t)=(sin⁡2πtπt)cos⁡(38πt−π/2)h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2) produces an output xo(t)x_{o}(t). The expression for xo(t)x_{o}(t) is _____\_\_\_\_\_.
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Let m(t)m(t) be a strictly band-limited signal with bandwidth BB and energy EE. Assuming ω0=10B\omega_{0}=10 B, the energy in the m(t)cos⁡ω0tm(t) \cos \omega_{0} t is
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
The Fourier transform X(ω)X(\omega) of x(t)=e−t2x(t)=e^{-t^{2}} is Note: ∫−∞∞e−y2dy=π\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, periodic (iii) Discrete, aperiodic (c) Discrete, aperiodic (iv) Discrete, periodic (d) Discrete, periodic
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMSQ · 1 mark
For a real signal, which of the following is/are valid power spectral density/densities?
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Let x1(t)\mathrm{x}_1(\mathrm{t}) and x2(t)\mathrm{x}_2(\mathrm{t}) be two band-limited signals having bandwidth B=4π×103  rad/sB=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s} each. In the figure below, the Nyquist sampling frequency, in rad/s\mathrm{rad} / \mathrm{s}, required to sample y(t)y(\mathrm{t}), is
Official PYQ2022Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
The Fourier transform X(jω)X(j \omega) of the signal x(t)=t(1+t2)2x(t) = \frac{t}{(1+t^{2})^{2}} is ______________.
Official PYQ2021Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Consider a real-valued base-band signal x(t)x(t), band limited to 10 kHz\text{10 kHz}. The Nyquist rate for the signal y(t)=x(t)x(1+t2)y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac{t}{2} \right ) is
Official PYQ2021Networks, Signals and SystemsContinuous-time SignalsNAT · 2 marks
The exponential Fourier series representation of a continuous-time periodic signal x(t)x(t) is defined as x(t)=∑k=−∞∞akejkω0tx\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t} where ω0\omega _0 is the fundamental angular frequency of x(t)x(t) and the coefficients of the series are aka_{k}. The following information is given about x(t)x(t) and …
Official PYQ2020Networks, Signals and SystemsContinuous-time SignalsNAT · 2 marks
X(ω)X\left ( \omega \right ) is the Fourier transform of x(t)x(t) shown below. The value of ∫−∞∞∣X(ω)∣2dω\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega (rounded off to two decimal places) is ____________
Official PYQ2019Networks, Signals and SystemsContinuous-time SignalsNAT · 1 mark
Consider the signal f(t)=1+2cos⁡(πt)+3sin⁡(2π3t)+4cos⁡(π2t+π4)f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right), where tt is in seconds. Its fundamental time period, in seconds, is __________.