# 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 (*f*_{c}), can be rearranged as follows.

Equation 2.6 states the following.

ERB = {24.7 3 [(4.37 3 f_{c}) + 1]} Hz |
(A2.1) |

- where
*f*_{c}= the filter center frequency in kHz - ERB = the equivalent rectangular bandwidth in Hz
- equation valid for (100 Hz <
*ƒ*_{c}< 10,000 Hz)

Rearranging step by step to find *f*_{c} as a function of ERB:

Therefore:

Therefore:

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