Re: [Maxima-discuss] very simple Fourier series question

[Raymond T. <toy...@gm...>]

On Sun, Jan 9, 2022 at 12:29 PM <ng...@gm...> wrote:

> Sorry to interrupt the current thread of discussion. Here is a very simple
> question related to Fourier series. I guess I am missing something very
> basic either in Maxima or probably in theory - should the two curves not be
> on top of each other? Many thanks, Thomas
>
> /* test Fourier representation in Maxima e.g. */;
>
> a:0.5*%pi; b:1.5*%pi;
>
> /* sin cos fourier series */;
>
> sincos(t):= a*sin(t) + b*cos(t)$
>
> /* A phi fourier series */;
>
> A: sqrt(a^2+b^2); phi: -atan2(b,a);
>
> Aphi(t):= A*cos(t+phi)$
>
> /* plot: expect sincos and Aphi to be on top */;
>
> pm: []$ pm: endcons(sincos(t),pm)$ pm: endcons(Aphi(t),pm)$
>
> wxplot2d( pm, [t, 0., 2*%pi],grid2d )$
>

Your Aphi function is not the same as sincos.  You can see this with
trigexpand(Aphi).

I think your phi is backwards.  I think you want -atan(a,b) because a is
the sin factor so it's the y component and b is the cos factor so it's the
x component.  Making that change makes Aphi expand to sincos, as expected.


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-- 
Ray