Chapter 10: Processes of Perception and Analysis

Section 8: Auditory Perception

Sound compression

Sound compression has in practice mostly been applied to human speech. In typical voice coders (vocoders) 64k bits per second of digital data are obtained by sampling the original sound waveform 8000 times per second, and assigning one of 256 possible levels to each sample. (Since the 1960s, so-called mu-law companding has often been used, in which these levels are distributed exponentially in amplitude.) Encoding only differences between successive samples leads to perhaps a factor of 2 compression. Much more dramatic compression can be achieved by making an explicit model for speech sounds. Most common is to assume that within each phoneme-length chunk of a few tens of milliseconds the vocal tract acts like a linear filter excited either by pure tones or randomness. In so-called linear predictive coding (LPC) optimal parameters are found to make each sound sample be a linear combination of, say, 8 preceding samples. The residue from this procedure is then often fitted to a code book of possible forms, and the result is that intelligible speech can be obtained with as little as 3 kbps of data. Hardware implementations of LPC and related methods have been widespread since before the 1980s; software implementations are now becoming common. Music has in the past rarely been compressed, except insofar as it can be specified by a score. But recently the MP3 format associated with MPEG and largely based on LPC methods has begun to be used for compression of arbitrary sounds, and is increasingly applied to music.

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