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 x(n+t
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
music-dsp@music.columbia.edu
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
music-dsp@music.columbia.edu
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
music-dsp@music.columbia.edu
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
music-dsp@music.columbia.edu
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] = uniform_random(0,
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
---
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
�
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 av
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 Du
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 fu
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
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