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Equivalent Rectangular Bandwidth (ERB) Filter Bank

After the development of third-octave filter banks, psychoacousticians performed further studies to obtain more accurate estimates of the auditory filter bandwidths. Most recently, they arrived at a formula they use to refer to Equivalent Rectangular Bandwidth (ERB). While a formula to convert frequency values into ERB-based frequencies is provided in psychoacoustics laboratory assignment, the bandwidth of an ERB filter centered at a given frequency $f_c$ is

BW_{ERB} = 24.7 \left(0.00437 f_c + 1 \right).
\end{displaymath} (7)

It is important to note that the formula above converts a frequency (in Hz) to a bandwidth (also in Hz). To convert a frequency in Hz to a frequency in units of ERB-bands, the formula from psychoacoustics laboratory assignment should be used, namely
ERB_{rate} = 21.4 \log \left( 0.00437 f_c + 1 \right)
\end{displaymath} (8)

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Download aud_fb.pdf

``Auditory Filter Bank Lab'', by Ryan J. Cassidy and Julius O. Smith III,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Ryan J. Cassidy and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University