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.^[1]

$\frac{df}{dv} = 6.23 \cdot f^2 %2B 93.39 \cdot f %2B 28.52$

Solving this equation gives roughly the following relation between the ERB value $v$ and the frequency $f$ in Hz:

$v = 11.17268 \cdot \log\left(1 %2B \frac{46.06538 \cdot f}{f %2B 14678.49}\right)$

Or the converse:

$f = \frac{676170.4}{47.06538 - e^{0.08950404 \cdot v}} - 14678.49$

A newer approximation is:^[2]

$\frac{df}{dv} = 107.94 \cdot f %2B 24.7$

Reference

^ B.C.J. Moore and B.R. Glasberg, "Suggested formulae for calculating auditory-filter bandwidths and excitation patterns" Journal of the Acoustical Society of America 74: 750-753, 1983.
^ B.R. Glasberg and B.C.J. Moore, "Derivation of auditory filter shapes from notched-noise data", Hearing Research, Vol. 47, Issues 1-2, p. 103-138, 1990.

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Equivalent rectangular bandwidth

See also

Reference

External links