Re: [music-dsp] how to derive spectrum of random sample-and-hold noise?

>there is nothing *motivating* us to define Rx[k] = E{x[n] x[n+k]} except that we >expect that expectation value (which is an average) to be the same as the other definition Sure there is. That definition gets you everything you need to work out a whole list of major results (for example, optimal

Re: [music-dsp] how to derive spectrum of random sample-and-hold noise?

>no. we need ergodicity to take a definition of autocorrelation, which we are all familiar with: > Rx[k] = lim_{N->inf} 1/(2N+1) sum_{n=-N}^{+N} x[n] x[n+k] >and turn that into a probabilistic expression > Rx[k] = E{ x[n] x[n-k] } >which we can figger out with the joint p.d.f. That's one

Re: [music-dsp] confirm 2692e89dd013da35bd113d6f644fdcfa865054c3

Original Message Subject: Re: [music-dsp] confirm 2692e89dd013da35bd113d6f644fdcfa865054c3 From: "Douglas Repetto" Date: Thu, November 12, 2015 10:26 am To: "A discussion list for music-related DSP"

Re: [music-dsp] how to derive spectrum of random sample-and-hold noise?

Original Message Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold noise? From: "Ethan Duni" Date: Wed, November 11, 2015 7:36 pm To: "robert bristow-johnson"

Re: [music-dsp] how to derive spectrum of random sample-and-hold noise?

Original Message Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold noise? From: "Ethan Duni" Date: Wed, November 11, 2015 5:57 pm To: "robert bristow-johnson"

Re: [music-dsp] how to derive spectrum of random sample-and-hold noise?

>all ergodic processes are stationary. (not necessarily the other way around.) Ah, right, there is no constant mean for a time average to converge to if the process isn't stationary in the first place. Been a while since I worried about the details of ergodicity, mostly I have the intuitive