1. An implantable cochlear stimulation (ICS) system comprising: a microphone adapted to convert an acoustical signal to a broad spectrum electrical signal; a speech processor connected to the microphone and configured to subject the broad spectrum electrical signal to a linear compressive mapping function to map the broad spectrum electrical signal to a first mapped signal, process the first mapped signal with a number of bandpass filters to separate the first mapped signal into a plurality of frequency band output signals, subject the plurality of frequency band output signals to a non-linear compressive mapping function to map the plurality of frequency band output signals to a multiplicity of second mapped signals; and an electrode array adapted to electrically stimulate a cochlea with signals derived from the first mapped signal and the second mapped signals; wherein the speech processor is configured to subject the broad spectrum electrical signal to the linear compressive mapping function to map the broad spectrum electrical signal to the first mapped signal by detecting an envelope of the broad spectrum electrical signal to produce a detected envelope signal; generating a processed envelope signal that follows the detected envelope signal at a limited rate; and combining the processed envelope signal with the broad spectrum electrical signal to produce the first mapped signal.