GATE ECE

Sampling

Signals and Systems

(Past Years Questions)

Marks 1

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Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t}...
GATE ECE 2016 Set 3
A continuous -time function $$x\left( t \right)$$ is periodic with period $$T$$. The function is sampled uniformly with ...
GATE ECE 2016 Set 1
The signal $$\cos \left( {10\pi t + {\pi \over 4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. Th...
GATE ECE 2015 Set 2
Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \rig...
GATE ECE 2014 Set 3
A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$ ...
GATE ECE 2014 Set 3
Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and ...
GATE ECE 2014 Set 1
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the samplin...
GATE ECE 2013
Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^...
GATE ECE 2002
A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through
GATE ECE 2001
Flat top sampling of low pass signals
GATE ECE 1998
A 1.0 kHz signal is flat - top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangul...
GATE ECE 1995
Increased pulse-width in the flat-top sampling, leads to ...
GATE ECE 1994

Marks 2

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The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The...
GATE ECE 2017 Set 2
Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limit...
GATE ECE 2015 Set 3
The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \ove...
GATE ECE 2010
The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without ...
GATE ECE 2006
A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where $$g(t)\, = \,\,\sum\limits_{k = - \infty...
GATE ECE 2006
A 1 kHz sinusoidal signal is ideally sampled at 1500 samples /sec and the sampled signal is passed through an ideal low-...
GATE ECE 2004
Let x(t) = $$\,2\cos (800\pi t) + \cos (1400\pi t)$$. x(t) is sampled with the rectangular pulse train shown in figure. ...
GATE ECE 2003
A signal x(t) = 100 cos $$(24\pi \times {10^3})$$ t is ideally sampled with a sampling period of 50 $$\mu \sec $$ and t...
GATE ECE 2002
The Nyquist sampling interval, for the signal Sinc(700t) + Sinc(500t) is
GATE ECE 2001
The Nyquist sampling frequency (in Hz) of a signal given by $$16 \times {10^{4\,}}\,\sin {c^2}(400t)*{10^6}\,\sin {c^3}(...
GATE ECE 1999
A signal has frequency components from 300 Hz to 1.8 KHz. The minimum possible rate at which the signal has to be sample...
GATE ECE 1991
A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal ...
GATE ECE 1990
A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed th...
GATE ECE 1988

Marks 4

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A low pass signal x(t) has a spectrum given by $$X(f) = \left\{ {\matrix{ {1 - \left| f \right|/2000,} & {for\,\,\lef...
GATE ECE 1992

Marks 5

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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 tr...
GATE ECE 2000
A low pass signal m(t) band-limited to B Hz is sampled by a periodic rectangular pulse train, $${p_\tau }(t)$$ of period...
GATE ECE 1993

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