Please consider this:

A step at t=0 results in some spectrum. If you have an identical step
which occurs at some other time, the amplitude of the spectrum is the
same, but the phases are different, and the difference depends on the
time difference. In fact, a negative step will have the same spectral
amplitude as a positive step, but inverted phases when comparing two
steps at the same time. (Note this gives the right result when you
add a positive and negative step coincident in time.) When you add
the two steps (perhaps one positive at t=0 and one negative at t=tau,
producing a pulse of width tau, for example), you will get
cancellation at some frequencies and reinforcement at others. The
resulting spectrum, then, depends on the time difference between the
edges, because the relative phases depend on the time difference.
Having a repetitive waveform (that has always existed and always will)
results in full cancellation of all spectral components except at DC
and 1/repetition rate and all harmonics of 1/repetition rate. But the
amplitudes (and phases) of the harmonics still depend on the timings.

Another (equivalent) way to look at it is that an impulse has a flat
spectrum, independent of the position of the impulse, but the phase of
the spectral components depends on the position (time) of the impulse.
Any waveform may be decomposed into an infinite series of impulses.
Consideration of the phases will lead you to the same conclusion as
the comments in the paragraph above.

You can use the basic properties of the Fourier transform to
demonstrate all this numerically or analytically if you wish.

Cheers,
Tom

"Richard Fry" wrote in message ...
Why would varying the pulse width without changing the characteristics of
the pulse transitions (rise/fall) affect the harmonic content of the pulse?
No bandwidth and no harmonics at all are produced by the constant DC level
of the pulse before and after each transition.

Wouldn't the harmonic structure and bandwidth needed to produce/reproduce a
pulse be related only to the rise and fall times of that pulse, and the
transition shapes (sin^2, etc), and be independent of the width (time)
between the transitions?

RF

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