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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 Preview

Please see the attached file.

1. We can just use the properties of Fourier transform
Conjugate function

Time scaling

Time shifting


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

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.