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

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 \log\left(1 + \frac{46.06538 \cdot f}{f + 14678.49}\right)

Or the converse: :

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

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