# Fourier transform and energy

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I am trying to get a feel for Fourier transforms and would like some help.

Please show all work/explanations.

1. Let g(t) = x(2t) - x*(2t- 1/2T0), assume that X(jw) is known

Find G(jw) in terms of X(jw).

2. Let x(t) = 10sin(200t)/t

a) Find X(jw)

b) Let x(t) be the input to a continuous LTI system with impulse response h(t) = sin(100t)/t.

Find the output y(t)

c) Find the energy in x(t) and the energy in y(t).

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##### Solution Summary

If provides examples of finding the Fourier transform of the signal. Then, it shows how to apply Fourier transform to find the output of the system given the impulse response. The solution is detailed and well presented.

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1. We can just use the properties of Fourier transform

Conjugate function

Time scaling

Time shifting

So

Be careful with the last one, the time shifting is , and it ...

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