Consider a continuous-time finite-energy signal  whose Fourier transform vanishes outside the frequency interval , where  is in .

The signal  is uniformly sampled to obtain . Here,

with  being the Dirac impulse, , and . The sampled signal  is passed through an ideal lowpass filter  with cutoff frequency  and passband gain .

The output of the filter is given by ___________.

A continuous time signal is sampled at a rate of 15 Hz. The sampled signal  when passed through an LTI system with impulse response        

Produces an output The expression for is __________.

Let  and  be two band-limited signals having bandwidth  each. In the figure below, the Nyquist sampling frequency, in , required to sample , is