Inverse PSD
in [Matlab]
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From: sajad aghsizade on 22 Feb 2010 15:49 Dear all I have a SPD spectrogram, and need to convert it to time state spectrom. Upshot i need PSD inverse function. Thanks all, sajadagh20(a)gmail.com
From: Wayne King on 22 Feb 2010 16:16 sajad aghsizade <sajadagh20(a)gmail.com> wrote in message <79d5564a-fc6e-4841-a0eb-fac03397bbab(a)x22g2000yqx.googlegroups.com>... > Dear all > I have a SPD spectrogram, and need to convert it to time state > spectrom. > Upshot i need PSD inverse function. > Thanks all, > sajadagh20(a)gmail.com Hi Sajad, when you typed SPD, did you mean to type PSD? When you say you have a PSD spectrogram, are you saying that you have a matrix of power spectral density estimates (real-valued nonnegative functions of frequency) of segments of the signal? In case you only have PSD estimates, you can't get THE time signal because once you have something proportional to the modulus squared of the Fourier transform of the input, you have no phase information. Stated differently, there are an infinite number of time functions with the same PSD. You can use spectral factorization to find one such time function however. But you can't find a unique mapping. Wayne
From: Jomar Bueyes on 22 Feb 2010 16:30 On Feb 22, 4:16 pm, "Wayne King" <wmkin...(a)gmail.com> wrote: > sajad aghsizade <sajadag...(a)gmail.com> wrote in message <79d5564a-fc6e-4841-a0eb-fac03397b...(a)x22g2000yqx.googlegroups.com>... > > Dear all > > I have a SPD spectrogram, and need to convert it to time state > > spectrom. > > Upshot i need PSD inverse function. > > Thanks all, > > sajadag...(a)gmail.com > > Hi Sajad, when you typed SPD, did you mean to type PSD? When you say you have a PSD spectrogram, are you saying that you have a matrix of power spectral density estimates (real-valued nonnegative functions of frequency) of segments of the signal? In case you only have PSD estimates, you can't get THE time signal because once you have something proportional to the modulus squared of the Fourier transform of the input, you have no phase information. Stated differently, there are an infinite number of time functions with the same PSD. > > You can use spectral factorization to find one such time function however.. But you can't find a unique mapping. > > Wayne Furthermore, the power spectral density is an ensemble average. You cannot recover a signal from the average of several of them. HTH Jomar
From: Frank on 22 Feb 2010 17:15 > > Furthermore, the power spectral density is an ensemble average. > > HTH > > Jomar That doesn't have to be the case. The simplest PSD is abs(fft)^2. But like Wayne says, you lose all phase information by using the abs() function.
From: TideMan on 22 Feb 2010 17:19
On Feb 23, 10:30 am, Jomar Bueyes <jomarbue...(a)hotmail.com> wrote: > On Feb 22, 4:16 pm, "Wayne King" <wmkin...(a)gmail.com> wrote: > > > sajad aghsizade <sajadag...(a)gmail.com> wrote in message <79d5564a-fc6e-4841-a0eb-fac03397b...(a)x22g2000yqx.googlegroups.com>... > > > Dear all > > > I have a SPD spectrogram, and need to convert it to time state > > > spectrom. > > > Upshot i need PSD inverse function. > > > Thanks all, > > > sajadag...(a)gmail.com > > > Hi Sajad, when you typed SPD, did you mean to type PSD? When you say you have a PSD spectrogram, are you saying that you have a matrix of power spectral density estimates (real-valued nonnegative functions of frequency) of segments of the signal? In case you only have PSD estimates, you can't get THE time signal because once you have something proportional to the modulus squared of the Fourier transform of the input, you have no phase information. Stated differently, there are an infinite number of time functions with the same PSD. > > > You can use spectral factorization to find one such time function however. But you can't find a unique mapping. > > > Wayne > > Furthermore, the power spectral density is an ensemble average. You > cannot recover a signal from the average of several of them. > > HTH > > Jomar OTOH, you can realise a particular time series by synthesising the square root of the PSD with random phase, then inverse FFT. This time series has the same 2nd order statistics (including 2nd order Kolmogorov structure function) as the original time series that was used to obtain the PSD, but all internal structure has been destroyed, including any fractal properties and self-similarity. |