I want to create a sine wave but with harmonics (all - both odd and even) that roll off in amplitude (each harmonic is lower than the previous one starting with the fundamental and going up) but I want to do it linearly and not logarithmically... not sure if I said that right, but the way it would look in the spectrum filter... if you look at the tones (set the FFT size to 16) and you created a point on the top of each harmonic the line would be straight and not curving downward. Here's the expression I came up with so you can see what I mean, just paste this into the goldwave expression evaluator and enter like 110 into the "f" box (or whatever frequency you like):

Code: Select all

```
sqrt(1/10^((log(01)/log(2))*2))*sin(2*pi*t*f*01)+
sqrt(1/10^((log(02)/log(2))*2))*sin(2*pi*t*f*02)+
sqrt(1/10^((log(03)/log(2))*2))*sin(2*pi*t*f*03)+
sqrt(1/10^((log(04)/log(2))*2))*sin(2*pi*t*f*04)+
sqrt(1/10^((log(05)/log(2))*2))*sin(2*pi*t*f*05)+
sqrt(1/10^((log(06)/log(2))*2))*sin(2*pi*t*f*06)+
sqrt(1/10^((log(07)/log(2))*2))*sin(2*pi*t*f*07)+
sqrt(1/10^((log(08)/log(2))*2))*sin(2*pi*t*f*08)+
sqrt(1/10^((log(09)/log(2))*2))*sin(2*pi*t*f*09)+
sqrt(1/10^((log(10)/log(2))*2))*sin(2*pi*t*f*10)+
sqrt(1/10^((log(11)/log(2))*2))*sin(2*pi*t*f*11)+
sqrt(1/10^((log(12)/log(2))*2))*sin(2*pi*t*f*12)+
sqrt(1/10^((log(13)/log(2))*2))*sin(2*pi*t*f*13)+
sqrt(1/10^((log(14)/log(2))*2))*sin(2*pi*t*f*14)+
sqrt(1/10^((log(15)/log(2))*2))*sin(2*pi*t*f*15)+
sqrt(1/10^((log(16)/log(2))*2))*sin(2*pi*t*f*16)+
sqrt(1/10^((log(17)/log(2))*2))*sin(2*pi*t*f*17)+
sqrt(1/10^((log(18)/log(2))*2))*sin(2*pi*t*f*18)+
sqrt(1/10^((log(19)/log(2))*2))*sin(2*pi*t*f*19)+
sqrt(1/10^((log(20)/log(2))*2))*sin(2*pi*t*f*20)+
sqrt(1/10^((log(21)/log(2))*2))*sin(2*pi*t*f*21)+
sqrt(1/10^((log(22)/log(2))*2))*sin(2*pi*t*f*22)+
sqrt(1/10^((log(23)/log(2))*2))*sin(2*pi*t*f*23)+
sqrt(1/10^((log(24)/log(2))*2))*sin(2*pi*t*f*24)+
sqrt(1/10^((log(25)/log(2))*2))*sin(2*pi*t*f*25)+
sqrt(1/10^((log(26)/log(2))*2))*sin(2*pi*t*f*26)+
sqrt(1/10^((log(27)/log(2))*2))*sin(2*pi*t*f*27)+
sqrt(1/10^((log(28)/log(2))*2))*sin(2*pi*t*f*28)+
sqrt(1/10^((log(29)/log(2))*2))*sin(2*pi*t*f*29)+
sqrt(1/10^((log(30)/log(2))*2))*sin(2*pi*t*f*30)+
sqrt(1/10^((log(31)/log(2))*2))*sin(2*pi*t*f*31)+
sqrt(1/10^((log(32)/log(2))*2))*sin(2*pi*t*f*32)
```

So those good at math might already know exactly what I'm trying to achieve now by seeing the math I'm using...

Well of course if I wanted to do more than 32 harmonics it would take forever to type by hand! So I was wondering if anyone good with math knows an expression that would generate harmonics all the way up to the nyquist frequency automatically and in a shorter expression?

And then if possible to also have the expression set so that one of the x or y variables could control the factor at which the harmonics roll off.

If someone could come up with an expression for me that could achieve this, I'd be very grateful!