Audio and speech compression systems have suffered several characteristic deficiencies. Single-channel compression systems cannot compress wideband signals without suffering from either spectral distortion or the inability to respond quickly to fast transients. When the input signal contains noise in addition to the desired speech signal, single-channel systems unnecessarily attenuate speech information. Single-channel compressors cannot compress the input signal differentially as a function of frequency. Multichannel compressors are capable of different levels of compression as a function of frequency. However, standard multichannel compressors unnecessarily attenuate important information about the shape of the short-term speech spectrum. This has resulted in poorer speech perception when using standard multichannel systems as compared with single-channel compression systems. A more general form of multichannel compression can emphasize information about the shape of the short-term speech spectrum. Susceptibility to many forms of noise is also reduced with such multichannel systems. Spectral distortion and undesired rapid overshoots and undershoots of signal level, characteristic of many single- and multi-channel systems, can be substantially reduced with such systems.