In article <1136d214-a420-4ef7-a1db-ed10303a1651@27g2000hsf.googlegroups.com>, DigitalSignal <digitalsignal999@yahoo.com> wrote:> It is a general question. We make dynamic signal analyzers. In a > signal analyzer, the typical waveform signa sources include sine, > white noise, swept sine, saw tooth, square etc.. The white noise is > always Gaussian type (with Kuotosis 3). This signal is usually > generated by summing up a few uniformly distributed random numbers. In > order to simulate what is happenning in the physical world, some users > ask for a random signal of which the Kuotosis is larger than 3. We > don't have a easy way to generate such as signal. > > James > www.go-ci.comthere are other ways, one of which is completely general, to get a normal variate from a uniform distribution. more importantly, if you need to generate some non-gaussian variate, you need to know the general transformation. you could look in "numerical recipes". for a normal (i.e. gaussian) distribution, the (moment coefficient of) kurtosis is always 3, independent of mean and variance. your title � non-gaussian � suggests that you know this. about all that comes to mind is: look at families of distributions, say the Pearson's, to see if something has a plausible kurtosis and shape. once you have the probability distribution, you can apply the general method of generating variates from a uniform distribution. vale, rip -- NB eddress is r i p 1 AT c o m c a s t DOT n e t
Generating non-Gaussian signal
Started by ●July 6, 2008
Reply by ●July 12, 20082008-07-12
Reply by ●July 12, 20082008-07-12
On 10 Jul., 22:21, DigitalSignal <digitalsignal...@yahoo.com> wrote:> It is a general question. We make dynamic signal analyzers. In a > signal analyzer, the typical waveform signa sources include sine, > white noise, swept sine, saw tooth, square etc.. The white noise is > always Gaussian type (with Kuotosis 3). This signal is usually > generated by summing up a few uniformly distributed random numbers. In > order to simulate what is happenning in the physical world, some users > ask for a random signal of which the Kuotosis is larger than 3. We > don't have a easy way to generate such as signal. > > Jameswww.go-ci.comYou could sample values according the following distribution: http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VII_distribution In this description the parameter m is connected to the kurtosis, and if m->infty you get a normal-distribution. One method to sample values to an arbitrariy distribtution f(x) is: http://en.wikipedia.org/wiki/Rejection_sampling Greetings, Uwe
Reply by ●July 12, 20082008-07-12
On 12 Jul., 12:03, Uwe Schmitt <rocksportroc...@googlemail.com> wrote:> On 10 Jul., 22:21, DigitalSignal <digitalsignal...@yahoo.com> wrote: > > > It is a general question. We make dynamic signal analyzers. In a > > signal analyzer, the typical waveform signa sources include sine, > > white noise, swept sine, saw tooth, square etc.. The white noise is > > always Gaussian type (with Kuotosis 3). This signal is usually > > generated by summing up a few uniformly distributed random numbers. In > > order to simulate what is happenning in the physical world, some users > > ask for a random signal of which the Kuotosis is larger than 3. We > > don't have a easy way to generate such as signal. > > > Jameswww.go-ci.com > > You could sample values according the following distribution: > > � �http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VI... > > In this description the parameter m is connected to the kurtosis, and > if m->infty > you get a normal-distribution. > > One method to sample values to an arbitrariy distribtution f(x) is: > > � � �http://en.wikipedia.org/wiki/Rejection_sampling >Look at GNU Scientific Library (GSL) which has lots of random generators. Greetings, Uwe
Reply by ●July 12, 20082008-07-12
Thank you all for the insights and comments. They are really helpful. Let me go further for this question: How to generate a random process of which both its PSD (Power Spectral Density) and Kurtosis can be controlled? A traditional method is that to apply a uniformed randomized phase to the defined PSD and conduct inverse FFT to create the time signal. Unfortunately this method always create Gaussian distributed time signal. James www.go-ci.com
Reply by ●July 12, 20082008-07-12
On Jul 12, 8:18 am, DigitalSignal <digitalsignal...@yahoo.com> wrote:> Thank you all for the insights and comments. They are really helpful. > Let me go further for this question:> How to generate a random process of which both its PSD (Power Spectral > Density) and Kurtosis can be controlled? A traditional method is that > to apply a uniformed randomized phase to the defined PSD and conduct > inverse FFT to create the time signal. Unfortunately this method > always create Gaussian distributed time signal. > > Jameswww.go-ci.comYou could try: http://www.engineers.auckland.ac.nz/~aste127/Jies97.pdf Of course, to find this you would have had to Google on controlled kurtosis. Dale B. Dalrymple
Reply by ●July 13, 20082008-07-13
Thank you again. I met with the author a while back and we had an argument. He uses multiple sine tones to create a random-look deterministic signal of which the Kurtosis is controlled. I said it is not a real random signal... But his approach is certainly one worth considering... James www.go-ci.com
Reply by ●July 13, 20082008-07-13
DigitalSignal wrote:> Thank you again. I met with the author a while back and we had an > argument. He uses multiple sine tones to create a random-look > deterministic signal of which the Kurtosis is controlled. I said it is > not a real random signal... > But his approach is certainly one worth considering... > > James > www.go-ci.comNo sequence that can be reproduced without being copied is truly random. What did you mean? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
