I have PSD data as a 1D array, function of frequency(rad/sec). It is like powerspectrum for damped oscillator.
Considering 3 modes, PSD is shown here.
I want to generate noise time series which should have PSD exactly like this. Power of the signal should be similar with the power calculated using PSD.
If some filter will be applied on white noise than it will change the power. One way I thought is to get band limited white noise for band of 1000 rad/sec and in this way I cover 10^3 to 10^7 range and then I will sum up all the noises. But it will be very very time consuming (10^4 such steps) and I also don't know how to get band limited white noise.
I am very new regarding this field. Can someone please tell me, how I can I do this in Mathematica? It will be very helpful to me.