Equivalent rectangular bandwidth

The ERB scale is a method for determining the equivalent rectangular bandwidth of sound filters ( auditory filters ) for electronic speech recognition or speech synthesis. ERB is a coming from the English abbreviation for Equivalent Rectangular Bandwidth ( about: equivalent rectangular bandwidth), which belongs to psychoacoustics.

The effects caused by sound loudness impression of the overall loudness is calculated in psychoacoustics by adding the induced into ERB frequency groups partial loudness. This gained with bandstop noise filter shape must be converted so that both filters have the same amount of energy happen to white noise in a corresponding rectangular filter shape. So we obtain the equivalent rectangular bandwidth ERB in which increases with the center frequency of the auditory filter. The formula for the ERB Berb factor f is a function of frequency:

Berb = 24.7 · ( 4.37 · f 1)

Here Berb in Hz and f is in kHz. You can use any frequency in this formula because it applies to every point on the basilar membrane. The ERB scale contains 40 levels in the frequency range up to 16 kHz.

The bandwidth of the auditory filter is referred to as critical bands. They are divided in 24 such groups. For critical bands are two scales: The Bark scale ( mel scale ) and the ERB scale. The critical bandwidth decreases with frequency, i.e., the higher the frequency, the more likely two adjacent tones of the same auditory filter can be processed.

Resolved this equation gives roughly the relationship between Berb and the frequency f in Hz:

Or as a reversal:

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