IEC Standard Weightings

Transfer functions:

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

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

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

$H_Z(s)={\displaystyle \frac{(2\pi \cdot 46066\mathrm{Hz}{)}^2{s}^2}{(s+2\pi \cdot 4.34\mathrm{Hz}{)}^2(s+2\pi \cdot 46066\mathrm{Hz}{)}^2}}$

$H_K(s)={\displaystyle \frac{1.5848634463348217s^2+18886.914378028894s+1.1260607147003824\times {10}^8}{s^2+15004.846526655707s+1.1259450726979023\times {10}^8}}$

$\times {\displaystyle \frac{1.0049948987146884s^2}{s^2+478.91221140843305s+57414.259359025615}}\times {10}^{-0.691/20}$

$\times {\displaystyle \frac{(2\pi \cdot 46066\mathrm{Hz}{)}^2}{(s+2\pi \cdot 46066\mathrm{Hz}{)}^2}}$

*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