(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x(t) is input into a perfect lowpass filter with frequency response H(ω), having a bandwidth of BHz and a passband gain of 1. For B = (2πT)^{-1}Hz, calculate the ratio of the output signal energy to the input signal energy.

2. Relevant equations

x(t) = Ae^{-|t|/T}

3. The attempt at a solution

I got |x(jω)| = A/(1+jω)

Using input energy W_{i}= (1/pi)[itex]\int[/itex]^{[itex]\infty[/itex]}_{0}|x(jω)|^{2}I got Wi to be A^{2}/2

The output energy W_{o}= (1/pi)[itex]\int[/itex]^{[itex]\infty[/itex]}_{0}|x_{o}(jω)|^{2}, where x_{o}(jω) = X(jω)H(jω)

but I'm unable to find any equation which links the frequency response to the bandwidth in order to get the output energy. I have that |H(ω)| = gain which in this instance is = 1. Is that all I need? I've a feeling I'm missing something very basic here. Any hints or clues appreciated!!

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# Electronic Signal and System problem: Ratio of signal energy

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