Sorry Tony, but krw is correct on this one.
Fourier postulated that every periodic wave could be represented by the
sum of a series of sinusoidal waves.
So far as I know, the vice versa isn't true. You can't represent a
sinusoidal wave as the sum of a series of square waves or saw tooth
waves or any other kind of wave (spherical wave) for that matter..
'A Pictorial Introduction to Fourier Analysis/Synthesis'
If that were the case, then anyone explaining Fourier Synthesis would
make the point loud and clear that you can represent any periodic wave
as the sum of a series of ANY KIND of wave, square, sinusoidal,
sawtooth, take your pick. But they don't say that. They say that you
can represent any periodic wave as the sum of a series of sinusoidal
waves, and they stop there.
That is exactly what a college professor wrote a paper on, over 50 years
ago. As I recall, he used a series of step functions to synthesize
other waveforms, and suggested that the process was not restricted to
sine and step.
My memory is getting dim, but I think the paper was written by Dr. Wayne
Chen, who became chairman of the department of Electrical Engineering at
the University of Florida in the late 1960s.
I think the mathematics involved in the use of sine waves may be much
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