# Questions & Answers of Sampling theorem

## Weightage of Sampling theorem

Total 6 Questions have been asked from Sampling theorem topic of Signals and Systems subject in previous GATE papers. Average marks 1.33.

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23 Hz. The fundamental frequency (in Hz) of the output is _________

Consider the signal $x\left(t\right)=\mathrm{cos}\left(6\mathrm{\pi t}\right)+\mathrm{sin}\left(8\mathrm{\pi t}\right)$, where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y\left(t\right)=x\left(2t+5\right)$ is

The signal $\mathrm{cos}\left(10\mathrm{\pi t}+\frac{\mathrm{\pi }}{4}\right)$ is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $\left(\frac{\mathrm{sin}\left(\mathrm{\pi t}\right)}{\mathrm{\pi t}}\right)\mathrm{cos}\left(40\mathrm{\pi t}-\frac{\mathrm{\pi }}{2}\right)$ . The filter output is

Consider a continuous-time signal defined as
$x\left(t\right)=\left(\frac{\sin\left(\pi t/2\right)}{\left(\pi t/2\right)}\right)\ast\sum_\limits{n=-\infty}^\infty\delta\left(t-10n\right)$
where '*' denotes the convolution operation and $t$ is in seconds. The Nyquist sampling rate (in samples/sec) for $x\left(t\right)$ is ___________.

An LTI system having transfer function $\frac{{s}^{2}+1}{{s}^{2}+2s+1}$ and input x(t)=sin(t+1) is in steady state. The output is sampled at a rate ωs rad/s to obtain the final output {y(k)}. Which of the following is true?