Contents Introduction
Multi-channel dynamic-range compression is an important feature in hearing aids [1]. One aspect of designing a multichannel compressor is to match the frequency resolution of the digital system to the resolution of the human auditory system. Digital frequency analysis, such as the discrete Fourier transform, typically provides constant-bandwidth frequency resolution. The frequency resolution of the human auditory system, however, is more accurately modeled by a filter bank having a nearly constant bandwidth at low frequencies but with bandwidth becoming proportional to frequency as the frequency increases [2], [3]. The mismatch between digital and auditory frequency analysis can be greatly reduced if the conventional uniform frequency analysis is replaced by a warped frequency analysis. Frequency warping uses a conformal mapping to give a non-uniform spacing of frequency samples around the unit circle in the complex-z plane [4], [5], [6]. With an appropriate choice of the parameters governing the conformal mapping [5], the reallocation of frequency samples comes very close to the Bark frequency scale [2] used to describe the auditory frequency representation. Frequency warping therefore allows the design of digital audio systems [6] and hearing aids [7] that have uniform time sampling but which have a frequency representation similar to that of the human auditory system.
