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.
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