Richard,

I think I see the problem here. The Fourier transform considers its
input over all time, from the beginning of time until eons into the
future. Its output is a frequency-domain spectrum which is
time-independent. That spectrum exists for all time, unchanging, to
accurately represent the input waveform. So from a Fourier transform
standpoint, there is not a spectrum associated with an edge, and a
different spectrum associated with "flat" parts of the waveform. The
integral runs from minus infinity to plus infinity. And to the degree
you've done the math exactly, you can exactly reconstruct the whole
input over all time from that single spectrum.

Of course, our practical approximations to the Fourier transform have
to limit the time over which the input is considered. So with a
modern "FFT spectrum analyzer," for example, you would indeed get zero
output when the input is zero, an interesting spectrum when the input
takes a step, and a simple DC output when the input is the flat DC
level after the step has been taken. If you get into using such an
analyzer, please do take the time to learn about that approximation to
the Fourier transform, and also about "windowing" and why it's needed
and how to select the proper window for what you're doing.

Cheers,
Tom

"Richard Fry" wrote in message ...
"Allen Windhorn" wrote:

One way to look at it is to consider the harmonics produced by all the
rising edges, and spearately consider the harmonics produced by the
falling edges. Both contain all of the harmonics, but since they are
displaced in phase, some of them get cancelled.

Obvious example: a square wave contains only odd harmonics.
________________

Would that not require the components of rising edges to be time-coincident
with a trailing edges? How could that occur when the these transitions
occur at different times?

RF

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