Timeline for PDF of discrete fourier transform of a sequence of gaussian random variables
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2011 at 20:08 | comment | added | Dan Becker | Oh, of course, I was was being dense late at night. I had already been following your approach, had realized that the determinant was just some function of N (that gets you the right normalization), but didn't see that you can just say that sum d_k^2 = 1/N^2 sum |f_k|^2 (by Parseval) = 1/N^2 sum a_k^2 + b_k^2, so you immediately get that both the real and imag components are gaussian distributed. Only half of the a_k and b_k are distinct, so you do have to be careful to get the right std dev for each particular component. | |
| Aug 26, 2011 at 7:36 | history | answered | fabee | CC BY-SA 3.0 |