FFT from incomplete data

On Tue, 13 Nov 2012 01:22:36 -0800 (PST), TomTurbo
<thomaslehner72@gmail.com> wrote:

>Hi, 
>
>I am computing the spectrum of a signal. Sometimes I don't have the full data 
>available because of communication losses. It is clear, that I can't show the 
>correct spectrum, but I want to show something that is as close as possible.
>
>Is there a mathematical correct way to do this ?
>
>Is there a way to do it without adding frequencies not present in the original signal ?

Hello Tom,
   I don't know what it means to "not have the full 
data available", but you might take a look at the 
article "Recovering Periodically-Spaced Missing Samples", 
by Andor Bariska in the November 2007 issue of the IEEE 
Signal Processing Magazine.

Good Luck,
[-Rick-]

I have the bad habit of using evolutionary algorithms (ES) to calculate Fourier coefficients. Does the FFT give the unique best fit to a power of 2 sequence of typical length (eg. 1024)?  If not then using something like ES would for sure be better though a bit time consuming (but I have fast algorithms).