Appendix 2: Solving the ERB Equation
To find the center frequency of the auditory filter whose critical bandwidth or ERB is equal to a given value, the ERB equation (Equation 2.6), which relates the critical bandwidth to the center frequency of the filter (fc), can be rearranged as follows.
Equation 2.6 states the following.
where fc = the filter center frequency in kHz
ERB = the equivalent rectangular bandwidth in Hz equation valid for (100 Hz < fc < 10000 Hz)
Rearranging step-by-step to find fc as a function of ERB:
Therefore:
Therefore:
So that:
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