Timeline for Fourier transform from the PSD
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2022 at 18:17 | comment | added | user1420303 | I meant FFT of the derivative of the autocorrelation function | |
| Feb 8, 2022 at 14:33 | comment | added | Hilmar | The FFT of autocorrelation function IS the PSD. They are the same thing | |
| Feb 8, 2022 at 11:44 | comment | added | user1420303 | It was a misunderstanding. I expected an imaginary spectrum, I just expected it to be near zero at low frequencies. Thanks to your comment I think I now understand that this does not happen simply because my system does not look sufficiently well represented by the model. I'm still not sure about something: Is it possible that what you meant in the second paragraph is multiplying by $j\omega$ to the FFT of the autocorrelation function ? (instead of to the PSD) | |
| Feb 8, 2022 at 3:07 | comment | added | Hilmar | Here is the thing: the ACF has a real valued spectrum. That means that the time derivate of the ACF has an imaginary spectrum. That's just the way the math works. If that doesn't fit your process you need a different model. | |
| Feb 7, 2022 at 18:33 | comment | added | user1420303 | +1 Thank you! 2nd paragraph: I also tried to avoid 2) and multiply $j \omega$ the result of 3). But I think that it is not the same as multiply $j \omega$ with the PSD as you said. What would I get with: $j \omega$ times PSD ???. ||| Last sentence: I did not understand that: do you mean the spectrum of the time derivative of the ACF? ||| I expect that the imaginary part of $Y(\omega)$ to be zero for small $\omega$ because I am studying procesess similar to those in en.wikipedia.org/wiki/Dielectric#Debye_relaxation (see $\varepsilon^{\prime\prime}$) | |
| Feb 7, 2022 at 18:12 | history | answered | Hilmar | CC BY-SA 4.0 |