GATE ECE
Signals and Systems
Sampling
Previous Years Questions

## Marks 1

Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t} \right),$$ where $$\,t$$ is i...
A continuous -time function $$x\left( t \right)$$ is periodic with period $$T$$. The function is sampled uniformly with a sampling period $${T_s}$$. ...
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...
A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$ where the baseband signal $$m... Let$$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \right)$$be sampled at$$20\,\,\,...
Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and $$y\left( t \right)$$ band - l...
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...
Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^{ + \infty } {\delta \left( {t... A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through Flat top sampling of low pass signals A 1.0 kHz signal is flat - top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangular LPF with cut - off frequenc... Increased pulse-width in the flat-top sampling, leads to ... ## Marks 2 The signal x(t) =$$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input t... Consider a continuous-time signal defined as$$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limits_{n = - \infty }^\infty {\d...
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
The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {... A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where$$g(t)\, = \,\,\sum\limits_{k = - \infty }^\infty {{{( - 10)}^k}\,\de...
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...
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 (...
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...
The Nyquist sampling interval, for the signal Sinc(700t) + Sinc(500t) is
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
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...
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 ...
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...

A low pass signal x(t) has a spectrum given by $$X(f) = \left\{ {\matrix{ {1 - \left| f \right|/2000,} & {for\,\,\left| f \right|\, \le \,2000\... ## Marks 5 A band limited signal x(t) with a spectrum X(f) as shown in Fig. a is processed as shown in Fig.b. p(t) is a periodic train of impulses as in Fig. c. ... A low pass signal m(t) band-limited to B Hz is sampled by a periodic rectangular pulse train,$${p_\tau }(t)$$of period$${T_s} = 1/(3B) sec. Assum...
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