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Thursday 8 April 2021

IEC Standard Weightings

Transfer functions:

\(H_A(s)=\dfrac{(12194\,\mathrm{Hz})^2\:\left(\frac{s}{2\pi}\right)^4\:\big/\: e^{-2.0000/20}}{(\frac{s}{2\pi}+20.6\,\mathrm{Hz})^2\,(\frac{s}{2\pi}+107.7\,\mathrm{Hz})\,(\frac{s}{2\pi}+ 737.9\,\mathrm{Hz})\,(\frac{s}{2\pi}+12194\,\mathrm{Hz})^2}\)

\(H_B(s)=\dfrac{(12194\,\mathrm{Hz})^2\:\left(\frac{s}{2\pi}\right)^3\:\big/\:  e^{-0.1697/20}}{\left(\frac{s}{2\pi}+20.6\,\mathrm{Hz}\right)^2\:\left(\frac{s}{2\pi}+158.5\,\mathrm{Hz}\right)\:\left(\frac{s}{2\pi}+12194\,\mathrm{Hz}\right)^2}\)

\(H_C(s)=\dfrac{(12194\,\mathrm{Hz})^2\:\left(\frac{s}{2\pi}\right)^2\:\big/\:  e^{-0.0619/20}}{\left(\frac{s}{2\pi}+20.6\,\mathrm{Hz}\right)^2\:\left(\frac{s}{2\pi}+12194\,\mathrm{Hz}\right)^2}\)

\(H_Z(s)=\dfrac{(2\pi\cdot 46066\,\mathrm{Hz})^2\:s^2}{(s+2\pi\cdot 4.34\,\mathrm{Hz})^2\:(s+2\pi\cdot 46066\,\mathrm{Hz})^2}\)

\(H_K(s)=\dfrac{1.5848634463348217\,s^2+18886.914378028894\,s+1.1260607147003824\times10^8}{s^2+15004.846526655707\,s+1.1259450726979023\times10^8}\)

\(\times\dfrac{1.0049948987146884\,s^2}{s^2+478.91221140843305\, s+57414.259359025615}\times 10^{-0.691/20}\)

\(\times\dfrac{(2\pi\cdot 46066\,\mathrm{Hz})^2}{(s+2\pi\cdot 46066\,\mathrm{Hz})^2}\)

*only A,C,K are standard

For RMS, after squaring, averaging technique may be RC LP filter.

for VU meter standard, RC = 0.0651442s equiv 2.44312 Hz

for loudness RMS (LKFS standard) RC = 0.392323 equiv 0.405674 Hz

https://en.wikipedia.org/wiki/A-weighting

https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-3-201208-S!!PDF-E.pdf

https://www.dsprelated.com/freebooks/filters/Low_High_Shelving_Filters.html

https://en.wikipedia.org/wiki/LKFS