[R] How to simulate quadratic phase couplilng

[Peter Yang]

Hi, I need to simulate the following two time series,

1. X=cos(omega1*t+phi1)+cos(omega2*t+phi2)+cos(omega3+phi3)
2. Y=cos(omega1*t+phi1)+cos(omega2*t+phi2)+cos(omega3+phi1+phi2)

where omega3=omega1+omega2 and phi1, phi2, phi3 are independent
uniform random variables from 0 to 2pi.

Question 1: when I simulate the time series, how should I make sure
that phi1, phi2, phi3 are independent?
Question 2: Since both sereis has non-zere values on FFT(omega1),
FFT(omega2), FFT(omega3), according to the estimation of 3rd-order  
periodgram=FFT(omega1)*FFT(omega2)*Conj(FFT(omega3)), then why the
third-order periodgram for X is 0 while not zero for Y.

Thanks a lot for your reply.