Fourier Synth Tool is up again at my website

[Paul Marossy]

Thanks to a member here (GGBB) I have this cool interactive tool up again at my website. He basically had to re-write most of the original Java applet so it would work in today's world. So what does it do? Well, it allows you to take a fundamental frequency and add various harmonics to it. You can see and hear what they do. I forgot what a cool tool that is!

If you're like me, you might be feeding a sine wave into a circuit & looking at the waveforms on your o'scope and not be quite sure what you're looking at... this tool can help with that, up to a point. I wonder if a different version could be made which would start with a clipped sine wave and then add harmonics. That would also be pretty rad.

To use it you'll need to enable Javascript. Doesn't work with every browser but does certainly work with MS Edge and Google Chrome. It won't load on my iPhone using Safari. YMMV.

http://www.diyguitarist.net/Misc/FourierTool%20Only.htm

[DrAlx]

Can use that to show how asymmetric clipping is linked to even harmonics.

Start with just B1 =100 (simple sine wave),
Now leaving B1=100,  see the effect of setting just one of the other B values to about 30.
Any B value you pick, either for odd harmonic (B3,B5,...) or even harmonic (B2, B4,...), will not give an asymmetric waveform.

You get an asymmetric waveform only by mixing B1 with even A-value(s).
For example, B1=100, with A2=30 looks a bit like asymmetric clipping.
As does (B1=100, A2=40, A4=8) which is clipped more.

You don't get an asymmetric wave if you mix B1=100 with any other B-values, or any odd A-values (A3, A5,...).

[PRR]

....Any B value you pick, either for odd harmonic (B3,B5,...) or even harmonic (B2, B4,...), will not give an asymmetric waveform....

It wants a 90 degree phase shift. Sin and Cos are 180 deg. The hack is 50Sin 50Cos which makes a 90 deg in-between wave. Now a slosh of 2nd makes a wacky-wave.

[DrAlx]

Actually not even a 90 degree phase shift is needed.
You can have no phase shift at all, and do A1=100, A2=30, with no B values, and still get a "clipped" waveform.
Doing the same thing using Sine waves instead (B1=100, B2=30) gives a waveform where there is no "clipping" but
upward and downward slopes of the waveform differ (sawtooth being the extreme case).
So even harmonics can show up in the waveform in two ways...

Either by asymmetry at the extremes of the wave (i.e. "clipping"), or by differences in the slope patterns of the rising and falling portions of the wave.  Odd harmonics alone won't give either of those effects, only even ones do.