Dear All, How to find a random signal vector whose power spectral density is known?? As we know FFT of auto correlation of any signal gives its power spectrum. If I go in the reverse direction, one solution could be, calculating IFFT and then reverse process of auto correlation. but I have no idea on how to find the reverse of auto correlation in matlab. any suggestions????? Kind regards Aamer
power spectral density
Started by ●January 25, 2007
Reply by ●January 25, 20072007-01-25
aamer wrote:> How to find a random signal vector whose power spectral density is known?? > As we know FFT of auto correlation of any signal gives its power spectrum. > If I go in the reverse direction, one solution could be, calculating IFFT > and then reverse process of auto correlation.What do you want to do? Are you looking for an MLS signal with a given power spectral density? This is simple. Set the amplitude in the frequency domain to match the desired spectral density and set the phase to random numbers. The IFFT of this coefficients will do the job. Marcel
Reply by ●January 25, 20072007-01-25
You won't find a unique answer because PSD is not the only factor to determine a signal. The other is its phase. In the other words, if you only know the PSD of a signal, you won't know what the signal is.
Reply by ●January 25, 20072007-01-25
On Jan 25, 4:22 pm, Marcel M=FCller <news.5.ma...@spamgourmet.org> wrote:> aamer wrote: > > How to find a random signal vector whose power spectral density is know=n??> > As we know FFT of auto correlation of any signal gives its power spectr=um.> > If I go in the reverse direction, one solution could be, calculating IF=FT> > and then reverse process of auto correlation.What do you want to do? Ar=e you looking for an MLS signal with a given> power spectral density? This is simple. Set the amplitude in the > frequency domain to match the desired spectral density and set the phase > to random numbers. The IFFT of this coefficients will do the job.This won't give you an MLS (if by MLS you mean Maximum-Length Sequence). An MLS only takes the values {-1,+1} in the time domain, and is flat in the frequency domain (other than being almost zero at DC). --=20 Oli
Reply by ●January 25, 20072007-01-25
"DigitalSignal" <digitalsignal999@yahoo.com> wrote in message news:1169745978.775191.135930@13g2000cwe.googlegroups.com...> You won't find a unique answer because PSD is not the only factor to > determine a signal. The other is its phase. In the other words, if you > only know the PSD of a signal, you won't know what the signal is. >If you inverse FFT PSD you get autocorrelation! Wiener-Kitchen theorem! F. -- Posted via a free Usenet account from http://www.teranews.com
Reply by ●January 25, 20072007-01-25
>aamer wrote: >> How to find a random signal vector whose power spectral density isknown??>> As we know FFT of auto correlation of any signal gives its powerspectrum.>> If I go in the reverse direction, one solution could be, calculatingIFFT>> and then reverse process of auto correlation. > >What do you want to do? Are you looking for an MLS signal with a given >power spectral density? This is simple. Set the amplitude in the >frequency domain to match the desired spectral density and set the phase>to random numbers. The IFFT of this coefficients will do the job. > > >Marcel >Hi Marcel, After going through ur reply, I got some idea to solve the problem. Let me put it here. I have power spectral density plot with frequency ranging from 0 to 1MHz on xaxis and power from 0 to -120dBc/Hz on yaxis. The task is to find a random signal with the PSD of above form. 1. convert power vector from dBc/Hz to linear. 2. apply root to find the amplitude 3. from r*exp(j*theta)(polar form),calculate the signal and convert into cartesian form as x+j*y.finally, apply IFFT to x+j*y which converts from frequency domain to time domain. where r is the amplitude calculated as in step 2 and theta is the angle generated by random vector of unit variance. Is it the right way??? king regards, Aamer
Reply by ●January 25, 20072007-01-25
On Thu, 25 Jan 2007 20:09:05 -0000, Fitlike Min <Fitlike@naeoption.com> wrote:> > "DigitalSignal" <digitalsignal999@yahoo.com> wrote in message > news:1169745978.775191.135930@13g2000cwe.googlegroups.com... >> You won't find a unique answer because PSD is not the only factor to >> determine a signal. The other is its phase. In the other words, if you >> only know the PSD of a signal, you won't know what the signal is. >> > > If you inverse FFT PSD you get autocorrelation! Wiener-Kitchen theorem!Indeed. But autocorrelation is not sufficient to determine the original signal. -- Oli
Reply by ●January 25, 20072007-01-25
On Jan 25, 4:23 pm, "Oli Charlesworth" <c...@olifilth.co.uk> wrote:> On Thu, 25 Jan 2007 20:09:05 -0000, Fitlike Min <Fitl...@naeoption.com> > wrote: > > > > > "DigitalSignal" <digitalsignal...@yahoo.com> wrote in message > >news:1169745978.775191.135930@13g2000cwe.googlegroups.com... > >> You won't find a unique answer because PSD is not the only factor to > >> determine a signal. The other is its phase. In the other words, if you > >> only know the PSD of a signal, you won't know what the signal is. > > > If you inverse FFT PSD you get autocorrelation! Wiener-Kitchen theorem!Indeed. But autocorrelation is not sufficient to determine the original > signal. > > -- > OliAamer didn't ask for "the" vector with a power spectral density. He asked for "a" vector. He might even want a number of them. This is not an unreasonable thing to do for testing purposes. What do you say Aamer? Are we being too helpful or not helpful enough? Dale B. Dalrymple http://dbdimages.com
Reply by ●January 26, 20072007-01-26
Reply by ●January 26, 20072007-01-26
Hi, Thanks for the efforts to solve the problem. As Oli said,only autocorrelation is not enough to know what the signal is. Hence,Wiener-Kinchein theorem cannot solve the problem. I got some idea. Wld like to share it. I have power spectral density plot with frequency ranging from 0 to 1MHz on xaxis and power from 0 to -120dBc/Hz on yaxis. The task is to find a random signal with the PSD of above form. 1. convert power vector from dBc/Hz to linear. 2. apply root to find the amplitude 3. from r*exp(j*theta)(polar form),calculate the signal and convert into cartesian form as x+j*y.finally, apply IFFT to x+j*y which converts from frequency domain to time domain. where r is the amplitude calculated as in step 2 and theta is the angle generated by random vector of unit variance. Is it the right way??? regards, Aamer.> > >On Jan 25, 4:23 pm, "Oli Charlesworth" <c...@olifilth.co.uk> wrote: >> On Thu, 25 Jan 2007 20:09:05 -0000, Fitlike Min<Fitl...@naeoption.com>>> wrote: >> >> >> >> > "DigitalSignal" <digitalsignal...@yahoo.com> wrote in message >> >news:1169745978.775191.135930@13g2000cwe.googlegroups.com... >> >> You won't find a unique answer because PSD is not the only factorto>> >> determine a signal. The other is its phase. In the other words, ifyou>> >> only know the PSD of a signal, you won't know what the signal is. >> >> > If you inverse FFT PSD you get autocorrelation! Wiener-Kitchentheorem!Indeed. But autocorrelation is not sufficient to determine the original>> signal. >> >> -- >> Oli > >Aamer didn't ask for "the" vector with a power spectral density. He >asked for "a" vector. He might even want a number of them. This is not >an unreasonable thing to do for testing purposes. What do you say >Aamer? > >Are we being too helpful or not helpful enough? > >Dale B. Dalrymple >http://dbdimages.com > >
