Equivalent rectangular bandwidth

For moderate sound levels and young listeners, Moore & Glasberg (1983) suggest that the bandwidth of human auditory filters can be approximated by the polynomial equation:

Eq.1

where F is the center frequency of the filter, in kHz, and ERB( F ) is the bandwidth of the filter in Hz. The approximation is based on the results of a number of published simultaneous masking experiments and is valid from 100, 6500Hz.

Seven years later, Glasberg & Moore (1990) published another, simpler approximation:

Eq.2

where f is in kHz and ERB(f) is also in kHz. The approximation is applicable at moderate sound levels and for values of f between 100 and 10000Hz.

The ERB-rate scale, or ERB-number scale, can be defined as a function ERBS(f) which returns the number of equivalent rectangular bandwidths below the given frequency f. The units of the ERB-number scale are known ERBs, or as Cams, following a suggestion by Hartmann. The scale can be constructed by solving the following differential system of equations:

The solution for ERBS(f) is the integral of the reciprocal of ERB(f) with the constant of integration set in such a way that ERBS(0) = 0.

Using the second order polynomial approximation (Eq.1) for ERB(f) yields:

where f is in kHz. The VOICEBOX speech processing toolbox for MATLAB implements the conversion and its inverse as:

where f is in Hz.

Using the linear approximation (Eq.2) for ERB(f) yields:

where f is in kHz.