List of practice Questions

Let $x(t)=\cos(10\pi t)+\cos(30\pi t)$ be sampled at $20$ Hz and reconstructed using an ideal low–pass filter with cut-off frequency of $20$ Hz. The frequency/frequencies present in the reconstructed signal is/are

A modulated signal is $y(t) = m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ kHz only. The minimum required rate (in kHz) at which $y(t)$ should be sampled to recover $m(t)$ is

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