Critical Band - Auditory Filters

Auditory Filters

Filters are used in many aspects of audiology and psychoacoustics including the peripheral auditory system. A filter is a device that boosts certain frequencies and attenuates others. In particular, a band-pass filter allows a range of frequencies within the bandwidth to pass through while stopping those outside the cut-off frequencies.

The shape and organisation of the basilar membrane means that different frequencies resonate particularly strongly at different points along the membrance. This leads to a tonotopic organisation of the sensitivity to frequency ranges along the membrane, which can be modeled as being an array of overlapping band-pass filters known as "auditory filters". The auditory filters are associated with points along the basilar membrane and determine the frequency selectivity of the cochlea, and therefore the listener’s discrimination between different sounds. They are non-linear, level-dependent and the bandwidth decreases from the base to apex of the cochlea as the tuning on the basilar membrane changes from high to low frequency. The bandwidth of the auditory filter is called the critical bandwidth, as first suggested by Fletcher (1940). If a signal and masker are presented simultaneously then only the masker frequencies falling within the critical bandwidth contribute to masking of the signal. The larger the critical bandwidth the lower the signal-to-noise ratio (SNR) and the more the signal is masked.

Another concept associated with the auditory filter is the equivalent rectangular bandwidth (ERB). The ERB shows the relationship between the auditory filter, frequency, and the critical bandwidth. An ERB passes the same amount of energy as the auditory filter it corresponds to and shows how it changes with input frequency. At low sound levels, the ERB is approximated by the following equation according to Glasberg and Moore:

ERB = 24.7*(4.37F + 1)

Where the ERB is in Hz and F is the centre frequency in kHz.

It is thought that each ERB is the equivalent of around 0.9mm on the basilar membrane. The ERB can be converted into a scale that relates to frequency and shows the position of the auditory filter along the basilar membrane. For example, an ERB number of 3.36 corresponds to a frequency at the apical end of the basilar membrane whereas an ERB number of 38.9 corresponds to the base and a value of 19.5 falls half-way between the two.

One filter type used to model the auditory filters is the gammatone filter. It provides a simple linear filter, which is therefore easy to implement, but cannot by itself account for nonlinear aspects of the auditory system; it is nevertheless used in a variety of models of the auditory system. Variations and improvements of the gammatone model of auditory filtering include the gammachirp filter, the all-pole and one-zero gammatone filters, the two-sided gammatone filter, and filter cascade models, and various level-dependent and dynamically nonlinear versions of these.