Acoustics and Psychoacoustics, 5th Edition

 

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 fc) + 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:

$\frac{\text{ERB}}{24.7}\text{=}\text{(4}\text{.37}\text{×}{f}_{\text{c}}\text{)}\text{+}\text{1}$

Therefore:

$\left(\frac{\text{ERB}}{24.7}\right)\text{-}\text{1}\text{=(}\text{4}\text{.37}\text{}\text{×}{f}_{\text{c}}\text{)}$

Therefore:

$[\frac{\left(\frac{\text{ERB}}{24.7}\right)-1}{4.37}$