Talk:Spectral density
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Physics is not the only field in which this concept appears, although I am not ready to write an article on its use in mathematics or statistics. Is any other Wikipedian? Michael Hardy 20:11 Mar 28, 2003 (UTC)
middle c
" then the pressure variations making up the sound wave would be the signal and "middle C and A" are in a sense the spectral density of the sound signal."
- What does that mean? - Omegatron 13:39, May 23, 2005 (UTC)
My idea is to write an article such that the first paragraph would be useful to the newcomer to the subject. I may not have succeeded here, so please fix it if you have a better idea. I just don't want to start the article with "In the space of Lebesgue integrable functions..." PAR 14:58, 23 May 2005 (UTC)
- yeah i hate that! i see what you're trying to say now... hmm... - Omegatron 16:57, May 23, 2005 (UTC)
stationarity
"If the signal is not stationary then the same methods used to calculate the spectral density can still be used, but the result cannot be called the spectral density."
- Are you sure of that? - Omegatron 13:39, May 23, 2005 (UTC)
Well, no. It was a line taken from the "power spectrum" article which I merged with this one. Let's check the definition. If you find it to be untrue, please delete it.
- I'll try to find something. -Omegatron 16:57, May 23, 2005 (UTC)
- It seems that this is true. They are considering the power spectrum to only apply to a stationary signal, and when you take a measurement of a non-stationary signal you are approximating. I know to take the spectrum of an audio clip with an FFT, you window the clip and either pad to infinity with zeros or loop to infinity, which sort of turns it into a stationary signal. - Omegatron 17:56, May 23, 2005 (UTC)
I'm starting to wonder about this. I think of a stationary process as a noise signal, with a constant average value, and a constant degree of correlation from one point to the next (with white noise having no correlation). I don't understand the meaning of stationary if its not with respect to noise, so I don't know whether the top statement is true or not. I'm not sure I understand what you mean by stationary in your example either. PAR 21:18, 23 May 2005 (UTC)
- Yeah, my concept of "stationarity" is not terribly well-defined, either. I'm pretty sure a sinusoid is stationary, and a square or triangle wave would be. As far as the power spectrum is concerned, stationary means that the spectrum will be the same no matter what section of the signal you window and measure. An audio signal would not be stationary, for instance. But I am thinking in terms of spectrograms and I'm not really sure of the mathematical foundations behind this. - Omegatron 21:25, May 23, 2005 (UTC)