ERB scale

The ERB scale (abbreviation for Equivalent Rectangular Bandwidth ) is a method in psychoacoustics for determining the equivalent rectangular bandwidth of tone filters ( auditory filters) for electronic speech recognition or speech synthesis .

By noise caused volume impression of the overall loudness is in psychoacoustics calculated by adding the partial loudness, in the individual inheritance frequency groups caused. This filter shape obtained with band stop noise must be converted into a corresponding rectangular filter shape so that both filters allow the same amount of energy to pass through in white noise . This gives the equivalent rectangular bandwidth in ERB, which increases with the center frequency of the auditory filter.

The formula for the ERB factor B _ERB in Hz as a function of the frequency f in kHz is:

{\ displaystyle B_ {ERB} = 24 {,} 7 \ ​​cdot (4 {,} 37 \ cdot f + 1)}

You can use any frequency in this formula, because it applies to every point on the basilar membrane . The ERB scale contains 40 steps in the frequency range up to 16 kHz.

The bandwidths of the auditory filters are called critical bands. There are 24 such groups to be distinguished. There are two scales for critical bands: the Bark scale ( Mel scale ) and the ERB scale. The critical bandwidth increases with frequency; H. the higher the frequency, the more likely two adjacent tones are processed by the same auditory filter.

{\ displaystyle {\ frac {\ mathrm {d} f} {\ mathrm {d} v}} = 6 {,} 23 \ cdot f ^ {2} +93 {,} 39 \ cdot f + 28 {,} 52}

This equation roughly gives the relationship between B _ERB and the frequency f in Hz:

{\ displaystyle B_ {ERB} = 11 {,} 17268 \ cdot \ log \ left (1 + {\ frac {46 {,} 06538 \ cdot f} {f + 14678 {,} 49}} \ right)}

Or the reverse:

{\ displaystyle f = {\ frac {676170 {,} 4} {47 {,} 06538-e ^ {0 {,} 08950404 \ cdot B_ {ERB}}}} - 14678 {,} 49}

Individual evidence

^ BC Moore, BR Glasberg: Suggested formulas for calculating auditory filter bandwidths and excitation patterns. In: The Journal of the Acoustical Society of America. Volume 74, Number 3, September 1983, pp. 750-753, PMID 6630731 .
↑ Gert tick awareness, Theo Herrmann, Werner German: Psycholinguistics . 2003, ISBN 3-11-011424-0 , pp. 207 ( online in Google book search).

Web links

[ERB-Moore-1] BC Moore, BR Glasberg: Suggested formulas for calculating auditory filter bandwidths and excitation patterns. In: The Journal of the Acoustical Society of America. Volume 74, Number 3, September 1983, pp. 750-753, PMID 6630731 .

[ERB-2] Gert tick awareness, Theo Herrmann, Werner German: Psycholinguistics . 2003, ISBN 3-11-011424-0 , pp. 207 ( online in Google book search).