Hang on, doesn't my test signal pass your criterion of being harmonic?
You could get it in the following way - make an offset square wave
S(t) = \sum_{n=0} sin( (2n-1) \omega t ) / (2n - 1) + C,
where C is adjusted so that the troughs of the square wave lie at zero
(maybe C = \pi/4). Now my test signal is
T(t) = S(t) sin(\omega t) + C',
where now C' is adjusted to remove the DC offset. But this function
contains only frequencies which are integer multiples of
\omega.
Actually this is clear from another point of view - if there were any
non-integral multiples of \omega the function would be quasi-periodic
rather than periodic.
--
opaqueice
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