Time domain noise from spectral density

In summary: But if you don't know what sort of process it is, you have to do something else.In summary, it is possible to generate a noise signal from a given spectral density by using a filter with the same transfer function as the spectral density. However, this method is only accurate if the noise is Gaussian. If the noise is not Gaussian, other methods must be used.
  • #1
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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  • #2
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
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
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
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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1. What is time domain noise from spectral density?

Time domain noise from spectral density is a measurement of the amount of noise present in a signal over a range of frequencies. It is typically represented as a graph that shows the noise amplitude versus frequency, and it allows scientists to analyze the noise characteristics of a signal.

2. How is time domain noise from spectral density measured?

Time domain noise from spectral density is measured using a spectrum analyzer, which is a device that can analyze a signal and display its frequency components. The spectrum analyzer measures the amplitude of the noise at different frequencies and plots it on a graph, giving a representation of the noise in the time domain.

3. What causes time domain noise in a signal?

There are several factors that can cause time domain noise in a signal, including electronic components, environmental factors, and interference from other signals. The noise can also be introduced during the signal processing and amplification stages.

4. How does time domain noise affect signal quality?

Time domain noise can degrade the quality of a signal by adding unwanted distortion and reducing the signal-to-noise ratio. This can make it more difficult to accurately interpret the signal and can lead to errors in data analysis and measurements.

5. How can time domain noise be reduced or eliminated?

There are several techniques that can be used to reduce or eliminate time domain noise in a signal. These include using low-noise components, shielding the signal from external interference, and using signal processing techniques such as filtering and averaging to remove the noise. It is also important to carefully design and optimize the signal path to minimize noise and interference.

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