# Equivalent rectangular bandwidth

The equivalent rectangular bandwidth or ERB is a measure used in psychoacoustics.

Researchers have derived a differential equation giving the ERB value [itex]v[itex] in Hz of a human auditory filter with a center frequency of [itex]f[itex] kHz

[itex]\frac{df}{dv} = 6.23 \cdot f^2 + 93.39 \cdot f + 28.52[itex]

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

[itex]v = 11.17268 \cdot \log\left(1 + \frac{46.06538 \cdot f}{f + 14678.49}\right)[itex]

Or the converse:

[itex]f = \frac{676170.4}{47.06538 - e^{0.08950404 \cdot v}} - 14678.49[itex]

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