# Closed form solution for this?

I have an equation describing a waveform:

f(x) = a0 * sin( x ) + a1 * sin( 2 * x + p1 ) + a2 * sin( 3 * x + p2 )

This is a periodic waveform with period 2 * pi

For fixed values of a0, a1, and a2, I would like to find values of p1
and p2 which maximise the asymmetry of the waveform. This would be:

max( f(x) ) - min( f(x) )

It is extremely easy for me to write a search based optimiser likely
to find an optimal or very close to optimal solution. But is there a
closed form solution to this?
.

## Relevant Pages

• Re: Closed form solution for this?
... and p2 which maximise the asymmetry of the waveform. ... to find an optimal or very close to optimal solution. ... closed form solution to this? ...
(sci.math.num-analysis)
• Re: Closed form solution for this?
... This is a periodic waveform with period 2 * pi ... and p2 which maximise the asymmetry of the waveform. ... to find an optimal or very close to optimal solution. ... closed form solution to this? ...
(sci.math.num-analysis)
• Re: Closed form solution for this?
... This is a periodic waveform with period 2 * pi ... and p2 which maximise the asymmetry of the waveform. ... to find an optimal or very close to optimal solution. ... closed form solution to this? ...
(sci.math.num-analysis)