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.

20 on this page

SubjectTopicYearType

A signal

x(t)

has a Fourier transform

X(\omega)

. If

x(t)

is a real and odd function of

t

, then

X(\omega)

The Nyquist sampling frequency (in

\mathrm{Hz}

) of a signal given by

6 \times 10^{4} \sin c^{2}(400 t)^{*} 10^{6} \sin c^{3}(100 t)

The Fourier series representation of an impules train denoted by

s(t)=\sum_{n=-\infty}^{n} d\left(t-n \mathrm{~T}_{0}\right) \text{ is given by }

A distorted sinusoid has the amplitudes

\mathrm{A}_{1}, \mathrm{A}_{2}, \text{A}_3 \ldots \ldots

of the fundamental, second harmonic, third harmonic, ...... respectively. The total harmonic distortion is

A periodic signal

x(t)

of period

T_0

is given by

x(t)= \begin{cases}1, & |t|<T_1 \\ 0, & T_1<|t|<\frac{T_0}{2}\end{cases}

The

\text{d.c}

. component of

x(t)

The trigonometric Fourier series of a periodic time function can have only

The Fourier transform of a voltage signal

x(t)

X(f)

. The unit of

|X(f)|

Flat top sampling of low pass signals

The Fourier transform of a function

x(t)

\mathrm{X}(f)

. The Fourier transform of

\frac{d \mathrm{X}(f)}{d f}

will be

The

\text{ACF}

of a rectangular pulse of duration

\mathrm{T}

The amplitude spectrum of a Gaussian pulse is

A deterministic signal has the power spectrum given in the figure is, The minimum sampling rate needed to completely represent this signal is

The function

f(t)

has the Fourier Transform

g(\omega)

. The Fourier Transform

f f(t) g(t)\left(=\int_{-\infty}^{\infty} g(t) e^{-j \omega t} d t\right)

The Fourier transform of a real-valued time signal has

The trigonometric Fourier series of an even function of time does not have the

The autocorrelation function of an energy signal has

1.0 \; \mathrm{kHz}

signal is flat-top sampled at the rate of

1800

samples sec and the samples are applied to an ideal rectangular

\text{LPF}

with cat-off frequency of

1100 \mathrm{~Hz}

, then the output of the filter contains.

The

\text{RMS}

value of a rectangular wave of period

T

, having a value of

+V

for a duration,

T_1(<T)

and

-V

for the duration,

T-T_1=T_2

, equals

Increased pulse-width in the flat-top sampling, leads to

The Fourice Series of a odd periọdic function, contains only