---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold noise? From: "Ethan Duni" <ethan.d...@gmail.com> Date: Tue, November 10, 2015 8:58 pm To: "A discussion list for music-related DSP" <music-dsp@music.columbia.edu> -------------------------------------------------------------------------- >>(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? all ergodic processes are stationary. �(not necessarily the other way around.) � the reason (besides forgetting stuff i learned 4 decades ago) i left out "stationary" was that i was sorta conflating the two. �i just wanted to be able to turn the time-averages in the whatever norm (and L^2 is as good as any) with probabilistic averages, which is the root meaning of the property "ergodic". �but probably "stationary" is a better (stronger) assumption to make. � > >>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? i'm thinking the same thing. �it's a discrete-time Markov process. �just model it and analyze it as such. assuming stationarity, we should be able to derive an autocorrelation function (and i think you guys did) and from that (and the DTFT) you have the (periodic) power spectrum. worry about frequency aliasing when you decide to output this to a DAC. -- � r b-j � � � � � � � � � r...@audioimagination.com � "Imagination is more important than knowledge."
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