Advanced Search

Question: Zero crossing determination

Question:Zero crossing determination

Jan GvK 20 Maple
rootof
November 30 2013
1

Hello,

Assume a periodic signal that is the sum of four sinusoidal signals, all with different frequency and phase. The fundamental frequency has phase=0, so at t=0 its value is 0 (a zero crossing point). I need to find the influence of the other frequency components on the zero crossing point in [seconds] as an analytical expression. I made the Maple script below to find out, but get a RootOf result. How can I solve this?

Thanks for your help!

> 

restart
> 

p := a*sin(omega[P]*t):
> 

q := b*sin(t*omega[Q]+phi[Q]):
> 

r := c*sin(t*omega[R]+phi[R]):
> 

s := d*sin(t*omega[S]+phi[S]):
> 

z := p+q+r+s

a*sin(omega[P]*t)+b*sin(t*omega[Q]+phi[Q])+c*sin(t*omega[R]+phi[R])+d*sin(t*omega[S]+phi[S])

 (1)
> 

solve(z, t)

RootOf(sin(_Z)*a+b*sin((_Z*omega[Q]+omega[P]*phi[Q])/omega[P])+c*sin((_Z*omega[R]+omega[P]*phi[R])/omega[P])+d*sin((_Z*omega[S]+omega[P]*phi[S])/omega[P]))/omega[P]

 (2)

``


Download 20131130_Zero_crossi.mw
Please Wait...