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Compensation for bilinear transform distortion of filter frequency response #241
Description
The use of the bilinear transform to derive filter coefficients (such as in signal.weigh) distorts the output frequency response from the desired analog response. This effect is negligible at lower frequencies, but becomes quite significant at higher ones, for example f4 = 12194 Hz in the IEC 61672-1 A-weighting filter.
Analytical techniques for compensating for the bilinear transform distortion can be found in:
Rimell A N et al, 2015. Design of digital filters for frequency weightings (A and C) required for risk assessments of workers exposed to noise. Industrial Health, 53, 21-27
and:
White, P R and Hammond, J K, 2004. Signal processing techniques. In: Advanced Applications in Acoustics, Noise and Vibration, chapter 1 (Fahy F and Walker, J, eds). Spon Press.
Activity
adrian-stepien commentedon Dec 1, 2020
Another possible solution is using Magnitude Invariance Method. It's described in this thesis (MATLAB code included):
Vadhavkar, Prathamesh R. - "Mapping controllers from the s-domain to the z-domain using magnitude invariance and phase invariance methods."