Equivalent rectangular bandwidth

Equivalent rectangular bandwidth

The equivalent rectangular bandwidth or ERB is a measure used in psychoacoustics, which gives an approximation to the bandwidths of the filters in human hearing, using the unrealistic but convenient simplification of modeling the filters as rectangular band-pass filters.

Researchers have derived a differential equation giving the ERB value v in Hz of a human auditory filter with a center frequency of f kHz:frac{df}{dv} = 6.23 cdot f^2 + 93.39 cdot f + 28.52

Solving this equation gives roughly the following relation between the ERB value v and the frequency f in Hz::v = 11.17268 cdot logleft(1 + frac{46.06538 cdot f}{f + 14678.49} ight)

Or the converse::f = frac{676170.4}{47.06538 - e^{0.08950404 cdot v - 14678.49

ee also

* Critical bands
* Bark scale


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