|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.
a sample spectrum
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?