FOURIER TRANSFORM
Octave summing is a useful but naive method of converting a given power spectrum into a signal. For reconstructing ocean waves, we are summing thousands of sine waves together, and that can get pretty slow.  In the early 1800's, a french mathematician named Jean Baptiste Joseph Fourier  did quite a bit of research into this, and he determined a method for doing this without actually summing,  a method called a Fourier transform.  Computer scientists have gotten this method to run very fast, taking a power spectrum and returning the signal with a fast Fourier transform.


power spectrum A
a sample spectrum

fourier signal
a reconstructed signal
so, a quick test of your understanding.
Given the below power spectrum, can you guess what the signal reconstructed with a fourier transform would be?

spike


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