I wonder how to generate a non-Gaussian signal of which the Kurtosis can be controlled. James www.go-ci.com
Generating non-Gaussian signal
Started by ●July 6, 2008
Reply by ●July 7, 20082008-07-07
On Jul 6, 7:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote:> I wonder how to generate a non-Gaussian signal of which the Kurtosis > can be controlled. > > Jameswww.go-ci.comI wonder what you have in your disposal to go about your task. I wonder how to help you if you don't say what you are starting with :-P.
Reply by ●July 10, 20082008-07-10
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.com
Reply by ●July 10, 20082008-07-10
On Jul 7, 6:42�am, julius <juli...@gmail.com> wrote:> On Jul 6, 7:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote: > > > I wonder how to generate a non-Gaussian signal of which the Kurtosis > > can be controlled. > > > Jameswww.go-ci.com > > I wonder what you have in your disposal to go about your task. > I wonder how to help you if you don't say what you are starting > with :-P.I usualy have food-related garbage in my disposal, but I turn on the water, flip the switch, and the garbage is gone. Turn off the switch, turn off the water, and I am on my way. Dirk
Reply by ●July 10, 20082008-07-10
DigitalSignal 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.Well, since a Gaussian (noise) is fully defined by its mean and variance, I guess you'll first to backtrace the Kurtosis to the variance. The, I still guess, multiplying the normal noise N(0,1) by the square root of the wanted variance "s", will give you N(0, s), hence the wanted Kurtosis. bye, -- piergiorgio
Reply by ●July 10, 20082008-07-10
On Jul 6, 5:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote:> I wonder how to generate a non-Gaussian signal of which the Kurtosis > can be controlled. > > Jameswww.go-ci.comA discussion of the motivation for and a claim of providing a kurtosis knob on the signal generator can be found at: http://www.testing-expo.com/usa/06conf/txna_pdfs/day_1/john_van_baron.pdf This can be found by performing a Google on the mystical words: controlled kurtosis. Whether a useful method will be shared with you is up to you to find. Dale B. Dalrymple http://dbdimages.com
Reply by ●July 10, 20082008-07-10
dbd <dbd@ieee.org> writes:> On Jul 6, 5:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote: >> I wonder how to generate a non-Gaussian signal of which the Kurtosis >> can be controlled. >> >> Jameswww.go-ci.com > > A discussion of the motivation for and a claim of providing a kurtosis > knob on the signal generator can be found at: > > http://www.testing-expo.com/usa/06conf/txna_pdfs/day_1/john_van_baron.pdfIn a nutshell, some real-world random variables aren't really Gaussian? -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●July 11, 20082008-07-11
On Jul 10, 4:56 pm, Randy Yates <ya...@ieee.org> wrote:> dbd <d...@ieee.org> writes: > > On Jul 6, 5:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote: > >> I wonder how to generate a non-Gaussian signal of which the Kurtosis > >> can be controlled. > > >> Jameswww.go-ci.com > > > A discussion of the motivation for and a claim of providing a kurtosis > > knob on the signal generator can be found at: > > >http://www.testing-expo.com/usa/06conf/txna_pdfs/day_1/john_van_baron... > > In a nutshell, some real-world random variables aren't really Gaussian? > -- > % Randy Yates % "My Shangri-la has gone away, fading like > %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" > %%% 919-577-9882 % > %%%% <ya...@ieee.org> % 'Shangri-La', *A New World Record*, ELOhttp://www.digitalsignallabs.comSee p7 of the citation or ponder why anyone would care about Gaussian mixture models or 'long-tailed' distributions if all real data were Gaussian. Dale B. Dalrymple
Reply by ●July 11, 20082008-07-11
On Jul 10, 7:56�pm, Randy Yates <ya...@ieee.org> wrote:> dbd <d...@ieee.org> writes: > > On Jul 6, 5:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote: > >> I wonder how to generate a non-Gaussian signal of which the Kurtosis > >> can be controlled. > > >> Jameswww.go-ci.com > > > A discussion of the motivation for and a claim of providing a kurtosis > > knob on the signal generator can be found at: > > >http://www.testing-expo.com/usa/06conf/txna_pdfs/day_1/john_van_baron... > > In a nutshell, some real-world random variables aren't really Gaussian?Hello Randy, Not everything is Gaussian. Radioactive decay is as good example of a non Gaussian process. Each particle (nucleus) has associated with it a negative exponential decay density. Then if you look at the interval times between decays in an ensemble of particles, then you will observe a nearly Poisson process. This you have likely heard as the audible "clicks" from a Geiger-Muller counter. Clay
Reply by ●July 11, 20082008-07-11
clay@claysturner.com writes:> On Jul 10, 7:56�pm, Randy Yates <ya...@ieee.org> wrote: >> dbd <d...@ieee.org> writes: >> > On Jul 6, 5:30 pm, DigitalSignal <digitalsignal...@yahoo.com> wrote: >> >> I wonder how to generate a non-Gaussian signal of which the Kurtosis >> >> can be controlled. >> >> >> Jameswww.go-ci.com >> >> > A discussion of the motivation for and a claim of providing a kurtosis >> > knob on the signal generator can be found at: >> >> >http://www.testing-expo.com/usa/06conf/txna_pdfs/day_1/john_van_baron... >> >> In a nutshell, some real-world random variables aren't really Gaussian? > > > Hello Randy, > > Not everything is Gaussian. Radioactive decay is as good example of a > non Gaussian process. Each particle (nucleus) has associated with it a > negative exponential decay density. Then if you look at the interval > times between decays in an ensemble of particles, then you will > observe a nearly Poisson process. This you have likely heard as the > audible "clicks" from a Geiger-Muller counter. > > ClayHi Clay, I didn't state my point very well. Yes, of course not all real-world random variables are Gaussian; some are not even close, as you point out. What I meant was that some real-world RV's that may appear to be Gaussian (or assumed to be) really aren't. -- % Randy Yates % "Remember the good old 1980's, when %% Fuquay-Varina, NC % things were so uncomplicated?" %%% 919-577-9882 % 'Ticket To The Moon' %%%% <yates@ieee.org> % *Time*, Electric Light Orchestra http://www.digitalsignallabs.com
