# Time domain noise from spectral density

1. Jul 19, 2013

### daudaudaudau

Hello. Say I have a given noise spectral density and I want to plot the random noise signal arising from this spectral density in the time domain. How can I generally accomplish this? For white noise, I would just pull numbers from a normal distribution, but I don't know what to do for non-white noise.

Best regards

2. Jul 19, 2013

### mathman

I can't remember all the details. The noise can be generated from a normal distribution, but there is a time correlation (Fourier transform of the spectrum) between samples at different times.

3. Jul 19, 2013

### jasonRF

In general the Fourier transform of the spectrum gives you the autocorrelation function. It is not so easy to figure out what sort of process will give rise to this autocorrelation function, though. If you have more information beyond just the spectrum (such as if the process is Gaussian) then you can do more.

jason

4. Jul 20, 2013

### daudaudaudau

What about making a filter, that has the same transfer function as the noise spectral density and then passing white noise through this filter? So if the spectral density is flat, you just get white noise again, if the filter is 1/f you get more low frequency content and less high frequency, and so on ... ?

5. Jul 20, 2013

### jasonRF

If you know that your noise is Gaussian then that is the correct thing to do; if your noise is not Gaussian then it is NOT the correct thing to do. That is what I was referring to above - it depends upon what you know about this process.

EDIT: I was sloppy in the above. If you know what sort of process this is (for example, Gaussian), you can make white noise then filter, just like you stated.

Last edited: Jul 20, 2013