Time domain noise from spectral density

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Discussion Overview

The discussion revolves around generating a random noise signal in the time domain from a given noise spectral density. Participants explore methods applicable to both white and non-white noise, considering the implications of the noise characteristics on the generation process.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about generating time domain noise from a spectral density, noting that for white noise, sampling from a normal distribution suffices, but is uncertain for non-white noise.
  • Another participant mentions that while noise can be generated from a normal distribution, time correlation exists between samples, which is related to the Fourier transform of the spectrum.
  • A different participant states that the Fourier transform of the spectrum yields the autocorrelation function, but determining the underlying process that produces this function can be complex. Additional information about the process, such as Gaussian characteristics, can aid in the generation.
  • One suggestion involves creating a filter that matches the transfer function of the noise spectral density and passing white noise through it, indicating that this method would yield different results based on the spectral density shape.
  • Another participant agrees with the filtering approach for Gaussian noise but cautions that it may not be appropriate for non-Gaussian noise, emphasizing the importance of understanding the noise process.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate methods for generating non-white noise, with some advocating for filtering techniques under certain conditions while others highlight the limitations based on the noise characteristics.

Contextual Notes

Participants note the dependence on the characteristics of the noise process, such as whether it is Gaussian, and the complexity involved in relating the spectral density to the time domain signal.

Who May Find This Useful

Individuals interested in signal processing, noise analysis, or those working with random processes in physics and engineering may find this discussion relevant.

daudaudaudau
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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
 
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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.
 
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
 
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 ... ?
 
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.
 
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