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endolith / waveform-analysis

Functions and scripts for analyzing waveforms, primarily audio. This is currently somewhat disorganized and unfinished.
MIT License
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Should removing DC component (substracting average) be after applying window? #20

Open zephray opened 2 years ago

zephray commented 2 years ago

I noticed that in the current code (https://github.com/endolith/waveform_analysis/blob/master/waveform_analysis/thd.py#L61) the DC component is removed before applying window. The calculated DC offset would be different after the window has been applied, causing the resulting FFT to have a rather large DC component in some cases.

For example, I have a 1kHz -3dBFS sine tone 32-bit wave file at 48kHz sample rate. I feed only the first 16K samples to the code (obviously the last sine cycle won't be complete, and that's why window functions are used). The result I got is a THD+N of -77.8dB while I expect it to be much better. If I increase the FFT points to 1M point, the THD+N gets improved to <-100dB. By inspecting the noise spectrum in the 16K point case, I noticed that the DC bin has a -77.8dB magnitude, explaining the rather poor THD+N. If I move the subtraction to after the windowing (windowed -= mean(windowed)), the THD+N immediately gets improved to -189.7dB, and the performance is consistent across different FFT sizes between 16K and 2M. (while in the previous cases, performances improve with larger FFT size).

These make sense to me however I am not sure if my modifications are correct or not. Do you have any idea about this?

endolith commented 2 years ago

@zephray Sorry for the delay.

Well, it needs to be removed before windowing or else the DC gets through the window:

Figure_1

Should it also be removed after windowing? Yeah, I think that's fine. DC shouldn't be part of the THD measurement. Analog THD+N meters have HPF at some point to remove it.

endolith commented 2 years ago

Probably the right way to do it is to emulate an analog analyzer and apply a bandpass filter with customizable cutoff frequencies

zephray commented 2 years ago

Thanks for the reply. Yes I later noticed this is also not correct, and ended up implementing an IIR HPF with 20Hz cutoff before sending the signal to windowing.