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 ___________.
For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then
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 ω_{s} rad/s to obtain the final output {y(k)}. Which of the following is true?