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

Wait, just realized I wrote that last part backwards. It should be: So in broad strokes, what you should see is a lowpass spectrum parameterized by P - for P very small, you approach a DC spectrum, and for P close to 1 you approach a spectrum that's flat. On Tue, Nov 3, 2015 at 10:26 AM, Ethan

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

Do you mean the literal Fourier spectrum of some realization of this process, or the power spectral density? I don't think you're going to get a closed-form expression for the former (it has a random component). For the latter what you need to do is work out an expression for the autocorrelation

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

Hi Everyone, Suppose that I generate a time series x[n] as follows: >>> P is a constant value between 0 and 1 At each time step n (n is an integer): r[n] = uniform_random(0, 1) x[n] = (r[n] <= P) ? uniform_random(-1, 1) : x[n-1] Where "(a) ? b : c" is the C ternary operator that takes on the

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

� i have to confess that this is hard and i don't have a concrete solution for you. �it seems to me that, by this description: � r[n] = uniform_random(0, 1) if (r[n] <= P) � �x[n] =�uniform_random(-1, 1); else �x[n] = x[n-1]; � from that, and from the assumption of ergodicity (where all time

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

On 4/11/2015 9:39 AM, robert bristow-johnson wrote: i have to confess that this is hard and i don't have a concrete solution for you. Knowing that this isn't well known helps. I have an idea (see below). It might be wrong. it seems to me that, by this description: r[n] =

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

On 4/11/2015 5:26 AM, Ethan Duni wrote: Do you mean the literal Fourier spectrum of some realization of this process, or the power spectral density? I don't think you're going to get a closed-form expression for the former (it has a random component). I am interested in the long-term magnitude

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: "Ross Bencina" Date: Tue, November 3, 2015 11:51 pm To: music-dsp@music.columbia.edu

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: "Ross Bencina" Date: Wed, November 4, 2015 12:22 am To: r...@audioimagination.com

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: "Ross Bencina" Date: Wed, November 4, 2015 12:22 am To: r...@audioimagination.com

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: "Ross Bencina" Date: Wed, November 4, 2015 12:22 am To: r...@audioimagination.com

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: "Ross Bencina" Date: Wed, November 4, 2015 12:22 am To: r...@audioimagination.com

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

How about this: For a lag of t, the probability that no new samples have been accepted is (1-P)^|t|. So the autocorrelation should be: AF(t) = E[x(n)x(n+t)] = (1-P)^|t| * E[x(n)^2] + (1 - (1-P)^|t|)*E[x(n)*x_new] The second term covers the case that a new sample has popped up, so x(n) and