Equal weight discretization. Please help!

Hello,

I am a brand new matlab user thus facing quite some difficulties. I have a function:

S(w)=5/16*Hs^2.*w.^4.*wp^(-5).*exp(-5/4.*(w./wp).^(-4));

Some of you will recognize it as a Pierson_Moskowitz wave energy spectrum. The thing is that I want to use equal area discretization in order to generate time signal. I think that using while loop could help me out. I could loop over frequency (w) axis as long as the integral of S(w) function is less than prescribed value (certain fraction of the total area under the curve). Then the problem comes in. I do not know how to tell Matlab that in the next loop it should start using frequency value (w) from the point where in previous loop the integral of S(w) reached desired value. Also, I do not know how to get the the frequency values at which while loop was met.

Please help me out or give some hint how to solve it as I have been struggling with this for a few week already.

I appreciate any help!

[Star Strider]

Would taking the inverse Fourier transform (or series) work to transform it into the time domain?

[Andrejus]

I think that it would not work in a way I want it to work. The Fourier transform would give time domain signal for equal frequecy increment (or any prescribed). What I want to do is to divide the area beneath the function in a way that each segment would have equal weight (area) beneath the curve.

Do I introduce the problem clearly?

Thanks!