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Solved Problems-19

A voltage, v(t) = 4e–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 Ω energy available at the output of the filter.
Let the output voltage is v0(t). The energy in v0(t) will be equal to the energy of that part of v(t), having frequency components in the intervals, 1 < f < 2 and –2 < f < –1.
Fourier transform of input,
Description: 4718.png
So, the total 1 Ω energy in the input signal is,
Description: 4724.png
or, Description: 4730.png

Total energy in the output is,
Description: 4736.png
Description: 4742.png
= 0.358 Joule

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