[sdiy] Re: Walsh Generator Release!!!

[Maciej Bartkowiak]

Magnus,

Are you talking about short-time Fourier transform 
on windowed data? If so, how could you compare it
to the continuous integral-based Laplace transform on
infinite support? It's unfair.

To make things clear, I am talking about the analytical
integral-based Fourier transformation which is fully revertible,
which means all the information of the signal is there, nothing
is lost in the Fourier domain, and the input signal may be 
obtained back through the inverse transformation.

Of course such transformation is not a tool aplicable for
practical measurements, due to infinite integration time
(the Laplace transformation shares the same drawback).
It is perfect for theoretical analysis of signals, though.

Both Laplace and Fourier transforms are complementary,
no one is a generalization or simplification of the other. The
domain of Laplace transform is a complex halfplane, but it
is limited to signals starting from zero, so you are basically
limited to the analysis of transients. Fourier is applicable to
all signals that are absolute integrable, and some others, too.
But its domain is only the imaginary axis. One cannot argue
any of them to be better than the other one.

Certainly, the usefullness of any transformation when applied
to signal analysis depends on our ability to understand and
properly interpret its output. In case of Fourier, one cannot 
neglect the phase spectra. I think this is a common mistake
in engineering practice, and your arguments come from this
bad experience.

regards,

MB