>Weighting a mean with log-magnitude can quickly lead to nonsense. To use log magnitude you'd first have to normalize it to look like a probability density (non-negative, sums to one). Meaning you add an offset so that the lowest value is zero, and then normalize. Obviously that puts restrictions on the class of signals it can handle - there can't be any zeros on the unit circle (in practice we'd just apply a minimum threshold at, say, -60dB or whatever) - and involves other complications (I'm not sure there's a sensible time-domain interpretation).
>I apply Occam's razor when making decisions about what metrics correspond most closely to nature What is the natural phenomenon that we're trying to model here? > log-magnitude is rarely sensible outside of perception modeling But isn't the goal here to estimate the "brightness" of a signal? Perceptual modelling is exactly why I bring log spectra up. E On Thu, Feb 18, 2016 at 7:42 AM, Evan Balster <e...@imitone.com> wrote: > Weighting a mean with log-magnitude can quickly lead to nonsense. Trivial > examples: > > - 0dB sine at 100hz, 6dB sine at 200hz --> log centroid is 200hz > - -6dB sine at 100hz, 12dB sine at 200hz --> log centroid is 300hz (!) > > Sanfillipo's adaptive median finding technique is still applicable, but > will produce the same result as a power or magnitude version. > > I apply Occam's razor when making decisions about what metrics correspond > most closely to nature. I choose the formula which is mathematically > simplest while utilizing operations that make sense for the dimensionality > of the operands and do not induce undue discontinuities. Power is simpler > to compute than magnitude, log-magnitude is rarely sensible outside of > perception modeling, and (unlike zero-crossing techniques) a small change > in the signal will always produce a proportionally small change in the > metrics. > > At next opportunity I should post up some code describing how to compute > higher moments with the differential brightness estimator. > > – Evan Balster > creator of imitone <http://imitone.com> > > On Thu, Feb 18, 2016 at 1:00 AM, Ethan Duni <ethan.d...@gmail.com> wrote: > >> >normalized to fundamental frequency or not >> >normalized (so that no pitch detector is needed)? >> >> Yeah tonal signals open up a whole other can of worms. I'd like to >> understand the broadband case first, with relatively simple spectral >> statistics that correspond to the clever time-domain estimators discussed >> so far in the thread. >> >> The ideas for time-domain approaches got me thinking about what the >> optimal time-domain approach would look like. But of course it depends on >> what definition of spectral centroid you use. For the mean of the power >> spectrum it seems relatively straightforward to get some tractable >> expressions - I guess this is the inspiration for the one based on an >> approximate differentiator. But I suspect that mean of the log power >> spectrum is more perceptually meaningful. >> >> E >> >> On Wed, Feb 17, 2016 at 8:34 PM, robert bristow-johnson < >> r...@audioimagination.com> wrote: >> >>> >>> >>> ---------------------------- Original Message >>> ---------------------------- >>> Subject: Re: [music-dsp] Cheap spectral centroid recipe >>> From: "Ethan Duni" <ethan.d...@gmail.com> >>> Date: Wed, February 17, 2016 11:21 pm >>> To: "A discussion list for music-related DSP" < >>> music-dsp@music.columbia.edu> >>> >>> -------------------------------------------------------------------------- >>> >>> >>It's essentially computing a frequency median, >>> >>rather than a frequency mean as is the case >>> >>with the derivative-power technique described >>> >> in my original approach. >>> > >>> > So I'm wondering, is there any consensus on what is the best measure of >>> > central tendency for a music signal spectrum? There's the median vs the >>> > mean (vs trimmed means, mode, etc). But what is the right domain in the >>> > first place: magnitude spectrum, power spectrum, log power spectrum or >>> ??? >>> >>> normalized to fundamental frequency or not normalized (so that no pitch >>> detector is needed)? should identical waveforms at higher pitches have the >>> same centroid parameter or a higher centroids? >>> >>> spectral "brightness" is a multi-dimensional perceptual parameter. you >>> can have two tones with the same spectral centroid (however consistent way >>> you measure it) and sound very different if the "second moment" or >>> "variance" is much different. >>> >>> >>> >>> -- >>> >>> >>> r b-j r...@audioimagination.com >>> >>> >>> >>> >>> "Imagination is more important than knowledge." >>> >>> _______________________________________________ >>> dupswapdrop: music-dsp mailing list >>> music-dsp@music.columbia.edu >>> https://lists.columbia.edu/mailman/listinfo/music-dsp >>> >> >> >> _______________________________________________ >> dupswapdrop: music-dsp mailing list >> music-dsp@music.columbia.edu >> https://lists.columbia.edu/mailman/listinfo/music-dsp >> > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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