# Solved Problems-19

Problems-19

A voltage,

*v*(*t*) = 4*e*^{â€“3t}*u*(*t*) volt is applied to the input of an ideal band-pass filter having a pass-band defined by 1 <*f*< 2 Hz. Calculate the total 1 Î© energy available at the output of the filter.Solution

Let the output voltage is
Fourier transform of input,

So, the total 1 Î© energy in the input signal is,
or,

Total energy in the output is,
= 0.358 Joule

*v*_{0}(*t*). The energy in*v*_{0}(*t*) will be equal to the energy of that part of*v*(*t*), having frequency components in the intervals, 1 <*f*< 2 and â€“2 <*f*< â€“1.Total energy in the output is,