A system for the compression and decompression of sections of audio files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of the selected basic waveforms is used to approximate a section of audio file. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed audio file. When the compressed audio file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to reproduce the original section of audio file.