Using A-Weighting on time signal

Question

Im trying to solve this for a couple of weeks now but it seems like Im not able to wrap my head around this. The task is pretty simple: Im getting a signal in voltage from a microfone and in the end I want to know how loud in dB(A) it is out there. There are so many problems I dont even know where to start. Lets begin with my idea.

1. Im converting the voltsignal into a signal in pascal [Pa].
2. Using a FFT on that signal so I know which frequencies im dealing with.
3. Then somehow I should implement the A-Weighting on that, but since im handling my values in [Pa] I cant just multiply or add my A-Weighning.
4. Going with an iFFT and getting back to my timesignal.
5. Going from Pa to dB.
6. Calculate RMS and Im done. (Hopefully)

The main problem is the A-Weighting. I realy dont get the idea how I can implement it on a live signal? And since the FFT leads to complex values Im also a little confused by that.

Maybe you get the idea/problem/workflow and help me to at least getting a little bit closer to the goal.

A little disclaimer, I am 100% new to the world of acoustics so please make sure to explain it like you would explain it a little child :D and Im programming with python.

Thanks in advance for your time!

Answer 1

To give you a short answer. This task can be done in only a few steps, utilizing the waveform_analysis package and Parseval's theorem.

The most simple implementation I can come up with is:

• Time domain A-weighting filtering the signal - Using this library -

import waveform_analysis
weighted_signal = waveform_analysis.A_weight(signal, fs)

• Take the RMS of the signal (utilizing that the power of the time domain equals the power of the frequency domain - Parseval's theorem). -

import numpy as np
rms_value = np.sqrt(np.mean(np.abs(weighted_signal)**2))

• Convert this amplitude to dB -

result = 20 * np.log10(rms_value)

This gives you the results in dB(A)FS, if you run these three snippets together.

To get the dB(A)Pa value, you need to know what 0 dBPa corresponds to in dBFS. This is usually done by having a calibrated source such as https://www.grasacoustics.com/products/calibration-equipment/product/756-42ag

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One flaw of this implementation is not pre-windowing the time signal. This is, on the other hand, not an issue for sufficently long signals.

Answer 2

Hello Christian Fichtelberg and welcome to StackOveflow. I believe your question could be answered more easily in DSP StackExchange but I will try to provide some quick and dirty answer.

In order to avoid taking the signal to the frequency domain, do the multiplication there (I urge you to the fact that convolution in the time domain - where your signal "resides" - is equivalent to multiplication in the frequency domain. If unfamiliar with this please have a quick look in Wikipedia's convolution page) you can implement the A-Weighting filter in the time-domain and perform some kind of convolution there.

I won't go into the details of the possible pros and cons of each method (time-domain convolution vs frequency domain multiplication). You could have a search on DSP SE or look into some textbook on DSP (such as Oppenheim's Digital Signal Processing, or an equivalent book by Proakis and Manolakis).

According to IEC 61672-1:2013 the digital filter should be "translated" from the analogue filter (a good way to do so is to use the bilinear transform). The proposed filter is a quite "simple" IIR (Infinite Impulse Response) filter.

I will skip the implementation here as it has been provided by others. Please find a MATLAB implementation, a Python implementation (most probably what you are seeking for your application), a quite "high-level" answer on DSP SE with some links and information on designing filters for arbitrary sample rates on DSP SE.

Finally, I would like to mention that if you manage to create a ("smooth enough") polynomial approximation to the curve of the A-Weighting filter you could possibly perform a frequency domain multiplication of the frequency response and the polynomial to change the magnitude only of the spectrum and then perform an iFFT to go back to time domain. This should most probably provide an approximation to the A-Weighted signal. Please note here that this is NOT the correct way to do filtering so treat it with caution (if you decide to try it at all) and only as a quick solution to perform some checks.