Chapter 10: Processes of Perception and Analysis

Section 8: Auditory Perception

Spectra [of sequences]

The spectra shown are given by Abs[Fourier[data]], where the symmetrical second half of this list is dropped in the pictures. Also of relevance are intensity or power spectra, obtained as the square of these spectra. These are related to the autocorrelation function according to

Fourier[list]^2== Fourier[ListConvolve[list, list, {1, 1}]]/Sqrt[Length[list]]

(See also page 1074.)

From Stephen Wolfram: A New Kind of Science [citation]