In dynamic-range compression, the input signal is multiplied by a time-varying gain.  The gain fluctuations introduce distortion, which may be audible for input signals such as white Gaussian noise. 
Dynamic-range compression uses estimates of the signal level to control a time-varying multiplicative gain applied to the signal.  The objective is to provide larger amounts of amplification to sounds at low intensities and reduced amplification to more-intense sounds.  A digital compressor typically operates on the signal in a multiplicity of frequency bands, with independent gains computed for each band.  The gains are normally controlled by the output of a peak detector, and the temporal dynamics of the compressor are thus specified by the peak-detector attack and release times. 
Because the compressor provides a multiplicative gain, it is a form of amplitude modulation.  Compression thus creates distortion side-bands that may be audible under some listening conditions.  The more rapidly the gain varies over time, the greater the magnitude of the sidebands and the greater the probability that the modulation will produce audible processing artifacts.  Thus increasing the compression ratio or reducing the attack and release times will increase the amount of perceptible distortion. 
An additional concern in a system using block processing is that the compressor gain changes do not occur smoothly over time but rather jump in value at the processing block boundaries.  Thus there is a discontinuity in the gain values that occurs at a periodic rate related to the processing block size.  For a block of 24 samples at a 16-kHz sampling rate, there will be a basic periodicity at 667 Hz that will also generate distortion.  Smoothing the gain over the duration of the processing block can remove the discontinuities, but is impractical in a digital hearing aid.  Low-pass filtering the gain values can also reduce the discontinuities, but at the expense of increasing the compression overshoot and reducing the ability of the hearing aid to quickly respond to sudden increases in the input sound level. 
There have recently been reports of audible compression modulation distortion in known compressors, and simulations have demonstrated audible modulation distortion.  These compression systems use ANSI attack times of 5 ms and ANSI release times of 70 ms (125 ms in the lowest frequency band).  Longer attack and release times would reduce the amount of audible distortion, but would increase the compression overshoot.  There is thus a need for a compression algorithm that reduces the audible modulation noise while preserving the ability to quickly reduce the gain for sudden increases in the input signal level. 
An example of a hearing aid with a compressor is disclosed in EP 1 448 022.