🚀 go-pugleaf

In article <15598@ucdavis.ucdavis.edu>
liuc@madrone.eecs.ucdavis.edu (Chia-Liang Liu Ka -Leung Lau)
writes:
>In article <TeNmoB1w164w@gmp.lonestar.org> greg@gmp.lonestar.org (G.R. Basile) writes:
>>
>>I agree. What has piqued my curiousity is how to derive an exact solution
>>of the power of the continuous time signal from the sampled data.

>The information provided by a digitized signal and its FFT is
>identical. Since you can not calculate the energy of a signal from
>its samples EXACTLY, you can't calculate it from its FFT either.

To me it is conceptually easy to obtain the EXACT power from the
samples.  Start by discretizing x(t) to get x[i].  By sampling at
more than four times the highest frequency in x(t), the sampling
criteria are satisfied for x^2(t).  The power in x(t) is the
integral from minus to plus infinity of x^2(t).  But x^2(t) is
equal to the sum of sinc functions weighted by x^2[i].  The
integral of the sinc function can be found in a table of
integrals, so the power simplifies to a weighted sum of x^2[i].
It is left as an exercise for the reader to carefully derive the
correct weights, but the principle is straight forward and it
clearly can be done.

Jim
--
James Szinger                        jim@fuji.eng.yale.edu