it's like a windowing function. except with hair on it.
(Installing 55 megabytes of signal processing libraries on the science box, so I might as well burble, right? I might accidentally say something useful.)

Oh, and by the way, I was wrong. This will not take a week. This stuff is getting intuitive. Look, we know that a pulse out of a square wave has a well-known spectrum. And f times g is the fourier transform of F convolved with G, so the part of a function that is between x1 and x2 has modified spectrum - take the original spectrum and convolve it with the spectrum of the square pulse.

Yeah, that made no sense. Again:

The Sinc and Rect functions are a fourier dual. Sinc looks rather like something you'd get from a one-or-maybe-two-slit laser experiment. Rect is a simple uniform, finite pulse - like a singleton from a square wave. A sharp, strong, skinny, brief, chirp of a Rect function has a weak, wide, long, slow Sinc dual... vice verse of course. When you're looking at the spectrum of a time series there is a basic problem: the full spectrum depends upon future events of which you can have no knowledge. So your time series has been multiplied by a Rect function before you even looked at it! The Rect function in question begins at zero, then at t_begin it hops up to one, then at t_present it's back to zero again. That multiplication in time space is a convolution in frequency space. All your frequencies will be smudged out by that Sinc. Clear, sharp spikes show up as sloping peaks instead.

Well, what's a gappy time series? It's just a bunch of Rects, right? And Fourier is a linear transform. Sinc and Sinc and Sinc and Sinc: the clear, sharp spikes turn into bizarre, wiggling plateaus. But if you know where the gaps are...

http://en.wikipedia.org/wiki/Least-squares_spectral_analysis
http://en.wikipedia.org/wiki/Fourier_transform
http://en.wikipedia.org/wiki/Fourier_series
http://en.wikipedia.org/wiki/Sinc_function

Install complete. Got to run.