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Version 5 (modified by Adam Frank, 10 years ago) ( diff )

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Fourier Transforms

The basic equation for the fourier transform.

with the inverse

Here we want to solve the signup function which is runs from -1 to 1 with a step at x=a

http://www.pas.rochester.edu/~afrank/Fig1.jpg

Use the derivative property of

Since derivative of f is the direct delta function

and

Thus we have

The next step is to define the Energy Spectral Density (ESD)

We use Parcivals Thm which tell us "energy" under the curve f(x)

Thus the ESD which we write as E(k) is

which for the sgn function is

So for a step function

Description of Problem

Results

Results

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