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I am looking at four different noise signals. I got them in a time domain and they are different. I went to the frequency domain and found the fft for all four signals. I got different shapes but I still cannot recognize which type of the noise (pink, blue, white, brown or what type)

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Could you please help me?

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Let me start with Noise 4. Noise 4 is "Zero-mean White Noise". White noise means the signal power is distributed across all frequencies evenly, which is what you see in the FFT result. From the histogram of the time signal we see that the signal is almost uniformly distributed, so close to a uniform white noise process. Although it appears closer to the sum of two independent Gaussian distributions, one with a positive non-zero mean and the other with a negative non-zero-mean, approximately +/- 0.25. (The result would be a zero-mean white noise random process).

Noise 1 is non-zero mean white noise, as evidenced by the spike at $F=0$ with a similar white noise spectrum everywhere else. From the histogram we see that it appears to be the sum of a zero-mean Gaussian White Noise (AWGN) process with a non-zero mean random process. The power level in the non-zero mean process is so small compared to the zero-mean AWGN process that we are unable to really discern further properties of that non-zero part that is added except for the mean which appears as a strong component in the FFT. Also from the histogram it looks like there really is very little signal component between the two, so the time domain plot appears as it does simply because you are connecting the dots as a line plot rather than plotting just the points (try using plot(time, noise, '.') to see just the waveform points. I suspect that it is a Gaussian distribution with a mean of 10 that is sparse compared to the non-mean noise waveform.

Noise 2 has been low pass filtered, and looks like it may have possibly been a white noise process that has been filtered by adding to itself after having been delayed by one sample. This could be called Pink Noise since the low frequency noise dominates (drawing an analogy from the visible light spectrum). From the histogram we see that this is well approximated as a Gaussian random process. So in this case it would be band-limited Gaussian noise.

Finally Noise 3 has a negative DC offset. Because of the scale, we cannot see if the noise process is pink or white (would need to zoom in on the FFT to observe that.) However from the histogram we see that it is a Gaussian distribution with non-zero mean.

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  • $\begingroup$ Thank you dear Dan Boschen for your answer. I went to the histogram to see if I can see more details there..what do you think of that. I have added a photo for the histogram for these four noise signals. $\endgroup$
    – SnowMan
    Dec 22, 2019 at 18:06
  • $\begingroup$ Yes the histogram of the time domain data would give more details as to the distribution (and then we could for example declare that one appears to be White Gaussian Noise: white given then the uniform power over frequency (on average) in the frequency domain and Gaussian given the Gaussian distribution in the time domain). Although I don't see the photo, are you sure you added it? The distribution for Noise 1 will be particularly interesting as it looks to be like there are two different noise processes added in that one. $\endgroup$ Dec 22, 2019 at 18:07
  • $\begingroup$ Dear Dan Boschen ,I have added the histogram photo if you can see it.Thanks! $\endgroup$
    – SnowMan
    Dec 22, 2019 at 18:16
  • $\begingroup$ Thanks I updated my comments on what we have learned from this new information. $\endgroup$ Dec 22, 2019 at 18:25
  • $\begingroup$ Dear Dan Boschen, I added the photo of a zoomed FFT for the third noise signal. Thanks for your support! $\endgroup$
    – SnowMan
    Dec 22, 2019 at 19:00

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