>(Semi-)stationarity, I'd say. Ergodicity is a weaker condition, true, >but it doesn't then really capture how your usual L^2 correlative >measures truly work.
I think we need both conditions, no? >Something like that, yes, except that you have to factor in aliasing. What aliasing? Isn't this process generated directly in the discrete time domain? E On Tue, Nov 10, 2015 at 5:43 PM, Sampo Syreeni <de...@iki.fi> wrote: > On 2015-11-04, robert bristow-johnson wrote: > > it is the correct way to characterize the spectra of random signals. the >> spectra (PSD) is the Fourier Transform of autocorrelation and is scaled as >> magnitude-squared. >> > > The normal way to derive the spectrum of S/H-noise goes a bit around these > kinds of considerations. It takes as given that we have a certain sampling > frequency, which is the same as the S/H frequency. Under that assumption, > sample-and-hold takes any value, and holds it constant for a sampling > period. You can model that by a convolution with a rectangular function > which takes the value one for one sampling period, and which is zero > everywhere else. Then the rest of the modelling has to do with normal > aliasing analysis. > > That's at least how they did it before the era of delta-sigma converters. > > with the assumption of ergodicity, [...] >> > > (Semi-)stationarity, I'd say. Ergodicity is a weaker condition, true, but > it doesn't then really capture how your usual L^2 correlative measures > truly work. > > i have a sneaky suspicion that this Markov process is gonna be something >> like pink noise. >> > > Something like that, yes, except that you have to factor in aliasing. > > > r[n] = uniform_random(0, 1) > if (r[n] <= P) > x[n] = uniform_random(-1, 1); > else > x[n] = x[n-1]; > > > If P==1, that give uniform white noise. If P==0, it yields a constant. If > P==.5, half of the time it holds the previous value. > > In a continuous time Markov process you'd get something like pink noise, > yes. But in a discrete time process you have to factor in aliasing. It goes > pretty bad, pretty fast. > > -- > Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front > +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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