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

x(f)

the fourier transform is

X(f)

. Then the inverse Fourier transform of

X(3 f+2)

The Fourier transform of a conjugate symmetric function is always

1 \; \mathrm{kHz}

sinusoidal signal is ideally sampled at

1500

samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey

800 \mathrm{~Hz}

. The output signal has the frequency

x(t)

y(t)

(with Fourier transforms

X(f)

Y(f)

respectively) be related as shown in the given figure. Then

Y(f)

Consider a system shown in the figure. Let

X(f)

Y(f)

denote the Fourier transforms of

X(t)

y(t)

respectively. The ideal HPF has the cutoff frequency

10 \mathrm{kHz}

. The positive frequencies where

Y(f)

has spectral peaks are

The Fourier series expansion of a real periodic signal with fundamental frequency

\mathrm{f}_0

g_p(t)=\sum_{n=-\infty}^{\infty} c_n e^{j 2 \pi n f_\omega t}

It is given that

c_3=3+j 5

c_{-3}

x(t)=2 \cos (800 \pi t)+\cos (1400 \pi t) . x(t)

is sampled with the rectangular pulse train shown in the figure. The only spectral components (in

\mathrm{kHz}

) present in the sampled signal in the frequency range

2.5 \; \mathrm{kHz}

3.5 \; \mathrm{kHz}

Consider a sampled signal

y(t)=5 \times 10^{\circ}

{ }^6 x(t) \sum_{(n-\infty}^{+\infty} \delta \left(t-n \mathrm{T}_x\right)

x(t)=10 \cos \left(8 \pi \times 10^3\right) t

T_s=100 \; \mu \mathrm{sec}

y(t)

is passed through an ideal lowpass filter with a cut-off frequency of 5

\mathrm{kHz}

, the output of the filter is

The Fourier transform

\mathrm{F}\left\{e^{-t} u(t)\right\}

\frac{1}{1+j 2 \pi f}

\mathrm{F}\left\{\frac{1}{1+j 2 \pi t}\right\}

Which of the following cannot be the Fourier series expansion of a periodic signal ?

x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t

is ideally sampled with a sampling period of

50 \; \mu \mathrm{sec}

and then passed through an ideal lowpass filter with cut-off frequency of

15 \; \mathrm{kHz}

. Which of the following frequencies is/are present at the filter output?

m(t)=\frac{2 \sin 2 \pi t}{t}, s(t)=\cos 200 \pi t

n(t)

=\frac{\sin 199 \pi t}{t}

y(t)

f(t)

E

, the energy of the signal

f(2 t)

A bandlimited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through

\delta(t)

denote the delta function. The value of the integral

\int_{-\infty}^{\infty} \delta(t) \cos \left(\frac{3 t}{2}\right) d t

The Nyquist sampling interval, for the signal

\text{Sin c } (700 t)+\text{Sin c } (500 t)

The Fourier Transform of the signal

x(t)=\mathrm{e}^{-3 \mathrm{t}^{2}}

is of the following form, where

A

B

The Hilbert transform of

\cos \omega_{1} t+\sin \omega_{2} t

(0, T)

each of two periodic waveforms

W_{1}

W_{2}

are shown in figure. The magnitudes of the

n

th Fourier series coefficients of

W_{1}

W_{2}

n \geq 1, n

odd, are respectively proportional to

A modulated signal is given by

s(t)=e^{-a t} \cos \left[\left(\omega_{c}+\Delta \omega\right) t\right] u(t),

a, \omega_{c}

\Delta \omega

are positive constants, and

\omega_{c} \gg \Delta \omega

. The complex envelope of

s(t)