# Sampling · Signals and Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2016 Set 3

Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t} \right),$$ where $$\,t$$ is i...

GATE ECE 2016 Set 1

A continuous -time function $$x\left( t \right)$$ is periodic with period $$T$$. The function is sampled uniformly with a sampling period $${T_s}$$. ...

GATE ECE 2015 Set 2

The signal $$\cos \left( {10\pi t + {\pi \over 4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed thr...

GATE ECE 2014 Set 3

Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \right)$$ be sampled at $$20\,\,\,...

GATE ECE 2014 Set 3

A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$ where the baseband signal $$m...

GATE ECE 2014 Set 1

Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and $$y\left( t \right)$$ band - l...

GATE ECE 2013

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid...

GATE ECE 2002

Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^{ + \infty } {\delta \left( {t...

GATE ECE 2001

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

GATE ECE 1998

Flat top sampling of low pass signals

GATE ECE 1995

A 1.0 kHz signal is flat - top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangular LPF with cut - off frequenc...

GATE ECE 1994

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

## Marks 2

GATE ECE 2017 Set 2

The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input t...

GATE ECE 2015 Set 3

Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limits_{n = - \infty }^\infty {\d...

GATE ECE 2010

The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \over {\pi \,t}}$$ is given by

GATE ECE 2006

The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {...

GATE ECE 2006

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\de...

GATE ECE 2004

A 1 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 frequ...

GATE ECE 2003

Let x(t) = $$\,2\cos (800\pi t) + \cos (1400\pi t)$$. x(t) is sampled with the rectangular pulse train shown in figure. The only spectral components (...

GATE ECE 2002

A signal x(t) = 100 cos $$(24\pi \times {10^3})$$ t is ideally sampled with a sampling period of 50 $$\mu \sec $$ and then passed through an ideal lo...

GATE ECE 2001

The Nyquist sampling interval, for the signal Sinc(700t) + Sinc(500t) is

GATE ECE 1999

The Nyquist sampling frequency (in Hz) of a signal given by $$16 \times {10^{4\,}}\,\sin {c^2}(400t)*{10^6}\,\sin {c^3}(100t)$$ is

GATE ECE 1991

A signal has frequency components from 300 Hz to 1.8 KHz. The minimum possible rate at which the signal has to be sampled is ______ (fill in the blank...

GATE ECE 1990

A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal is to be ideally sampled. The ...

GATE ECE 1988

A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed through a low pass filter with a...

## Marks 4

GATE ECE 1992

A low pass signal x(t) has a spectrum given by $$X(f) = \left\{ {\matrix{
{1 - \left| f \right|/2000,} & {for\,\,\left| f \right|\, \le \,2000\...

## Marks 5

GATE ECE 2000

A band limited signal x(t) with a spectrum X(f) as shown in Fig. a is processed as shown in Fig.b. p(t) is a periodic train of impulses as in Fig. c. ...

GATE ECE 1993

A low pass signal m(t) band-limited to B Hz is sampled by a periodic rectangular pulse train, $${p_\tau }(t)$$ of period $${T_s}$$ = 1/(3B) sec. Assum...