envelope rms implementation by Matlab

Question

I am trying to implement the moving RMS by Matlab.

x = randn(50, 1);
xRMS = sqrt(movmean(x.^2, 21));
xRMSref = envelope(x, 21, 'rms');
plot(xRMSref,'DisplayName','xRMSref');hold on;plot(xRMS,'DisplayName','xRMS');hold off;
legend()

Why my estimation differs from Matlab's?

Florian · Accepted Answer · 2020-09-24T14:52:34.783

3

That is because envelope centers the signal before computing the standard deviation and afterwards corrects for the mean. Try this instead:

x = randn(50, 1);
xRMS = sqrt(movmean(x.^2, 21));
xRMS_centered = sqrt(movmean((x-mean(x)).^2, 21)) + mean(x);
xRMSref = envelope(x, 21, 'rms');
plot(xRMSref,'x-','DisplayName','xRMSref');hold on;plot(xRMS,'o-','DisplayName','xRMS');plot(xRMS_centered,'s-','DisplayName','xRMS centered');hold off;
legend()

*edit: since you were asking why envelope behaves this way: I think it's because it tries to return an envelope of the signal. It actually comes with two output arguments, a lower and an upper envelope with the idea that the signal should be between the two. Clearly if that's what we want, we need to account for the mean. See example in the following figure:

If you didn't center, you wouldn't capture the local variation around the mean accordingly.

edited Sep 24 '20 at 14:52

answered Sep 24 '20 at 10:22

Florian

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any reason why they are doing it? Is their solution is better than mine? – Gideon Genadi Kogan Sep 24 '20 at 11:03
also, is there any reference for such practice? – Gideon Genadi Kogan Sep 24 '20 at 11:26
in RMS you don't remove the mean while when computing standard deviation you remove the mean... – Ben Sep 24 '20 at 13:38
@Ben but we are computing the rms rather than the std, right? – Gideon Genadi Kogan Sep 24 '20 at 13:42
the RMS includes the DC part. However, you called the Matlab envelope function. The envelope excludes the DC part. – Ben Sep 24 '20 at 13:59
@GideonGenadiKogan: I added some explanation and an example for why I think the centering is included in the `envelope` function. – Florian Sep 24 '20 at 14:53
@Florian Thanks a lot. It clarified everything – Gideon Genadi Kogan Sep 25 '20 at 07:49
You're welcome! Glad it helped. – Florian Sep 25 '20 at 07:55

envelope rms implementation by Matlab

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