Please excuse (and ignore) this if this is not the right place to ask this. I am an ecologists and need to generate a time series with a specific color or frequency spectra. I never learned how fourier transforms work in class and while I get the gist from reading there are so many subtleties that makes it hard to get it right unless one spends considerable time understanding it all. So I hope to get some help here. I want to be able to define minFreq, maxFreq, Nfreq, Variance and color. I do not want to generate a discrete time series but instead have a function that provides me with a continuous function over time, even if it is evaluated at a specific time. Also, I'd prefer to make this in the sine domain instead of complex. I want to get two vectors (amplitude, A and phase, P) by providing minFreq, maxFreq, Nfreq, Variance (of the time series) and color such that I can call T(t,A,P)=sum(A*sin(w*t+P)) with the output having the given variance and color I tried this code but does not have the properties I need and I probably made many errors in ignorance. N=64 k=1:N maxP=365 minP=1 k=linspace(minP,maxP,N) w=2*pi*k'./maxP b=1 p=rand(N,1)*2*pi a=ones(N,1).*(1./w.^(b/2)) for t=1:1000 T(t)=sum(a.*sin(t*w+p))./sum(a); end *slight edit* Any hints are greatly appreciated P.S. is it possible to define the vectors such that the generated time serie's variance is independent of the choice of Nfreq and color?