Simulating Sample Jitter
in [DSP]
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From: aruzinsky on 10 Feb 2010 11:45 On Feb 10, 10:40 am, aruzinsky <aruzin...(a)general-cathexis.com> wrote: > On Feb 9, 7:03 pm, pnachtwey <pnacht...(a)gmail.com> wrote: > > > Does anybody have a good way of simulating sample jitter? > > I want to beef up my simulations. Normal distribution isn't good > > enough because the distribution isn't skewed and it doesn't allow one > > to have a zero probability at 0 and almost 0 at some point in the > > future like 25 microseconds and then be able to adjust the where the > > peak probability is in between like at 6 microseconds. > > > Gamma or Beta distributions may work but they required a whole lot of > > calculations which slow down a simulation. Also they are hard to > > scale. > > > I have seen articles on the topic not specifically about the > > simulation function used, at least not good ones. > > > Peter Nachtwey > > Jitter PSFs are often, if not typically, spatially variant. > > Spatial variance can be seen in this example:http://www.general-cathexis.com/images/DSC00115.png Sorry, I thought I was in the image processing group.
From: Baron on 10 Feb 2010 12:28 "pnachtwey" <pnachtwey(a)gmail.com> wrote in message news:07d168e2-a5c1-43d8-ae78-e5f9735a1fd5(a)t31g2000prh.googlegroups.com... > Does anybody have a good way of simulating sample jitter? > I want to beef up my simulations. Normal distribution isn't good > enough because the distribution isn't skewed and it doesn't allow one > to have a zero probability at 0 and almost 0 at some point in the > future like 25 microseconds and then be able to adjust the where the > peak probability is in between like at 6 microseconds. > > Gamma or Beta distributions may work but they required a whole lot of > calculations which slow down a simulation. Also they are hard to > scale. > > I have seen articles on the topic not specifically about the > simulation function used, at least not good ones. > > Peter Nachtwey we usually modeled Jitter as a flat distribution
From: Tim Wescott on 10 Feb 2010 19:26 On Tue, 09 Feb 2010 17:03:56 -0800, pnachtwey wrote: > Does anybody have a good way of simulating sample jitter? I want to beef > up my simulations. Normal distribution isn't good enough because the > distribution isn't skewed and it doesn't allow one to have a zero > probability at 0 and almost 0 at some point in the future like 25 > microseconds and then be able to adjust the where the peak probability > is in between like at 6 microseconds. > > Gamma or Beta distributions may work but they required a whole lot of > calculations which slow down a simulation. Also they are hard to scale. > > I have seen articles on the topic not specifically about the simulation > function used, at least not good ones. > > Peter Nachtwey It sounds like you know the _way_ you want to simulate jitter, but are looking for good distributions to use that won't bring your simulation speed to it's knees -- is this correct? You could probably get by with something approximate -- what about a three or four point, piecewise linear function that operates on a uniform RV such as you'd get from 'rand'? -- www.wescottdesign.com
From: pnachtwey on 10 Feb 2010 22:50 On Feb 10, 4:26 pm, Tim Wescott <t...(a)seemywebsite.com> wrote: > On Tue, 09 Feb 2010 17:03:56 -0800, pnachtwey wrote: > > Does anybody have a good way of simulating sample jitter? I want to beef > > up my simulations. Normal distribution isn't good enough because the > > distribution isn't skewed and it doesn't allow one to have a zero > > probability at 0 and almost 0 at some point in the future like 25 > > microseconds and then be able to adjust the where the peak probability > > is in between like at 6 microseconds. > > > Gamma or Beta distributions may work but they required a whole lot of > > calculations which slow down a simulation. Also they are hard to scale. > > > I have seen articles on the topic not specifically about the simulation > > function used, at least not good ones. > > > Peter Nachtwey > > It sounds like you know the _way_ you want to simulate jitter, but are > looking for good distributions to use that won't bring your simulation > speed to it's knees -- is this correct? Yes > > You could probably get by with something approximate -- what about a > three or four point, piecewise linear function that operates on a uniform > RV such as you'd get from 'rand'? > > --www.wescottdesign.com OK, I have found out that what I am trying to do is not something that is cook book. I will probably using the technique Vladimir suggested where a random number generated is used to generate a number between 0 to 1 and then use that to index into a cumulative distribution function ( CDF ) that provides a profile I like that provides delays of 0 to say 25 microseconds with a peak around 6 microseconds. I agree that the distribution may be multi modal but like Tim said I don't to slow down my simulation too much. Peter Nachtwey
From: dave y. on 11 Feb 2010 16:33 On Tue, 9 Feb 2010 17:03:56 -0800 (PST), pnachtwey <pnachtwey(a)gmail.com> wrote: >Does anybody have a good way of simulating sample jitter? >I want to beef up my simulations. Normal distribution isn't good >enough because the distribution isn't skewed and it doesn't allow one >to have a zero probability at 0 and almost 0 at some point in the >future like 25 microseconds and then be able to adjust the where the >peak probability is in between like at 6 microseconds. > >Gamma or Beta distributions may work but they required a whole lot of >calculations which slow down a simulation. Also they are hard to >scale. > >I have seen articles on the topic not specifically about the >simulation function used, at least not good ones. > >Peter Nachtwey You might consider the Weibull distribution. It's quite simple, being defined by an exponential function, it's one sided, and it has a 'slope' parameter that yields a variety of distribution shapes. dave y.
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