A-Weighting Formula
A-weighting approximates the human ear's sensitivity and is widely used for SPL and environmental noise reporting.
Standard A-weighting response
The analog A-weighting curve defined in IEC 61672 uses a reference gain of 2.00 dB at 1 kHz. The magnitude response is typically expressed as:
Frequencies are in Hz. The constants are breakpoints in the analog model.
What the variables and constants mean
- f is the frequency in Hz where you want the weighting value.
- R_A(f) is the linear (not dB) magnitude response of the analog A-weighting curve.
- A(f) is the response in dB after applying the 2.00 dB normalization at 1 kHz.
- 20.6 Hz and 12194 Hz are the low and high corner frequencies of the main high-pass and low-pass sections.
- 107.7 Hz and 737.9 Hz are the mid-band shaping corners that make the response match human hearing.
- 12194^2 appears because the analog transfer function uses squared breakpoints in the numerator and denominator.
- f^4 in the numerator reflects the two zeros at DC that tilt the low-frequency response downward.
- + 2.00 dB is the standard reference adjustment so the curve is 0 dB at 1 kHz.
These constants come from the IEC 61672 analog specification and are defined so the response matches the historical A-weighting curve.
Without the +2.00 dB adjustment, the raw analog transfer function evaluates to about -2 dB at 1 kHz. The standard expects A-weighting to read 0 dB at 1 kHz so that broadband levels remain anchored to an unweighted reference at the calibration frequency. The +2.00 dB factor is therefore a normalization step: it aligns the curve with meter calibration practice and ensures A-weighted results are comparable across instruments and datasets.
Digital implementation notes
- Convert the analog transfer function to digital using a bilinear transform at the target sample rate.
- Use SOS form to improve numeric stability, especially at higher sample rates.
- Verify the response at 1 kHz equals 0 dB after the +2.00 dB normalization term.
Many DSP libraries include A-weighting helpers, but confirm their compliance with the target standard and sample rate.
Where A-weighting is used
- Environmental noise reporting and regulatory compliance.
- Building acoustics and HVAC noise measurements.
- Consumer product noise ratings (LAeq, LAF, etc.).
FAQ
Why does the A-weighting formula add 2.00 dB?
The raw analog transfer function evaluates to about -2 dB at 1 kHz. The +2.00 dB term normalizes the curve so A-weighting reads 0 dB at the 1 kHz calibration frequency, keeping results consistent across meters.
Where should I apply A-weighting in the processing chain?
Apply A-weighting either to the broadband time series before banding or to the band levels after filtering. The key is consistency with the reporting standard and ensuring the reference level is unchanged.