A signal $$x(t) = 2\cos (180\pi t)\cos (60\pi t)$$ is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz.

The maximum frequency present in the filtered signal in Hz is ___________ (Round off to the nearest integer).

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

An input signal x(t) = 2 + 5sin(100$$\mathrm\pi$$t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by $$$\frac{Y\left(z\right)}{X\left(z\right)}=\frac1N\left[\frac{1-z^{-N}}{1-z^{-1}}\right]$$$ where, N represents the number of samples per cycle. The output y(n) of the system under steady state is

A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) has a frequency of