Thread Subject: Energy Density Spectrum to Time Series

Hi,
   I need an application for which input is the Energy Density Spectrum as a function of "w" and output should be a time series.If any body does have any idea or code already done and verified,You may please share.

Thanks in advance.

"SmartEngineer" <smartengineer@mathworks.com> wrote in message <gh0r9m$hl6$1@fred.mathworks.com>...
> Hi,
> I need an application for which input is the Energy Density Spectrum as a function of "w" and output should be a time series.If any body does have any idea or code already done and verified,You may please share.
>
> Thanks in advance.

typically you go from an amplitude and phase representation back to a time series with ifft. but that requires both amplitude and phase to properly recreate the original wave. if the 'energy density' is just a magnitude you could try to use ifft, but without phase information it is unlikely that it would faithfully reproduce the original waveform. it would of course have the same spectrum magnitude, but not necessarily the the same as the original.

> typically you go from an amplitude and phase representation back to a time series with ifft. but that requires both amplitude and phase to properly recreate the original wave. if the 'energy density' is just a magnitude you could try to use ifft, but without phase information it is unlikely that it would faithfully reproduce the original waveform. it would of course have the same spectrum magnitude, but not necessarily the the same as the original.

Hello David
   
1. What I have is probably a magnitude spectrum...How about using a random phase.Does it help?

2. Also Can you please explain the last line "...it would of course have the same spectrum magnitude, but not necessarily the the same as the original."...Im not clear what actually you mean here

3. ifft of the Energy Density Function...does it directly give the time series?

Your suggestions will be very helpful.Thank you.

Regards

"SmartEngineer" <smartengineer@mathworks.com> wrote in message <gh2339$2fc$1@fred.mathworks.com>...
>
> > typically you go from an amplitude and phase representation back to a time series with ifft. but that requires both amplitude and phase to properly recreate the original wave. if the 'energy density' is just a magnitude you could try to use ifft, but without phase information it is unlikely that it would faithfully reproduce the original waveform. it would of course have the same spectrum magnitude, but not necessarily the the same as the original.
>
> Hello David
>
> 1. What I have is probably a magnitude spectrum...How about using a random phase.Does it help?
>
> 2. Also Can you please explain the last line "...it would of course have the same spectrum magnitude, but not necessarily the the same as the original."...Im not clear what actually you mean here
>
> 3. ifft of the Energy Density Function...does it directly give the time series?
>
> Your suggestions will be very helpful.Thank you.
>
> Regards

1. random phase is just as bad as no phase.
2. try taking a couple simple sin functions at different frequencies, add them together and do an fft, then take just the magnitude of the results... change the phase relation and you get the same magnitudes. do the ifft of any of the magnitudes and you will get back the same signal, but all the components will have zero phase.
3. yes and no, it will have to be scaled for the number of points... see the fft and ifft function descriptions and related discussion in the help. but remember, without the phase information you will never know exactly what the original time sequence looked like. you can recreate one that will give you the same magnitude of the spectrum, but without the phase infomation it can't be an exact reproduction.


also be careful about matlab's indexing on fft/ifft, since arrays are 1 based instead of 0 and can't have negative frequencies the results are shifted... be sure to look at fftshift/ifftshift to be sure you are getting the right results.

Thanks alot...That clear things for me.So,I understand I can get a time series corresponding to the magnitude spectrum and this time series may not necessarily be same each time we execute the application,unless the phase is defined.I hope Iam right.

And Thanks once again.