[sdiy] Harmonic bandwidth

[ASSI]

On Sonntag 06 Januar 2008, Ben Lincoln wrote:
> But when you instead change the phase of only some of the
> harmonics, the resulting waveforms are going to be different due to
> constructive and destructive interference.

Whoa, careful.  The waveform is different, yes - but due to 
superposition, not interference.  The whole theory of frequency 
analysis rests on the fact that waves at different frequencies don't 
interfere in a linear medium.

> In order to make sure I wasn't completely wrong, I tried this myself
> in Audacity - I started with two sine waves, 100Hz and 200Hz. In one
> copy of the project, I deleted a tiny piece of the 200Hz wave so that
> it was running at just less than 90 degrees ahead of the phase of the
> 100Hz wave. A/Bing the two it is easy to tell the difference. I tried
> it with some more complicated variations too, and the result was the
> same.

If you take care that audacity doesn't normalize the amplitudes, 
eliminate the DC offset error you just introduced and that there is 
also no overflow or clipping from adding the two waves you will most 
certainly not hear a difference.  You can test this most easily with a 
sawtooth, provided you can make a wave from a spectrum: a sawtooth has 
a 1/n spectrum.  If all the spectral coefficients have the same sign 
the resulting wave will actually look like a sawtooth.  When you flip 
the sign of any of the coefficients it doesn't necessarily look 
anything like a sawtooth anymore, but it still sounds like one.  If you 
do everything correctly and can still hear a difference, submit 
yourself to your favourite psychoacoustics lab - they will be really 
interested to run tests with you.


Achim.
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