# How to judge the percentage of white noise and color noise when using typical SDR enviroment?

Per this question,I understand different result when noise occurs in time domain and frequency domain.

As to the system,has antenna+upconveter+USRPB210+laptop,observe frequency around 75M HZ,bindwidth 16M.

How to judge the percentage of white noise and color noise when using typical SDR enviroment?

I understand different result when noise occurs in time domain and frequency domain.

That's not true for the noise power overall (Linearity of Fourier Transform), but:

of course, Fourier-transforming colored noise will¹ yield noise with a different spectral shape. You can't de-correlate it using a Fourier transform, so the percentage in uncorrelated (i.e., white) and colored noise will remain the same.

How to judge the percentage of white noise and color noise when using typical SDR enviroment?

Good, complicated question! In the end, it is equivalent to acquiring a PSD estimate, because the PSD is the Fourier transform of the autocorrelation function, and in the autocorrelation function, the amount of white noise can directly be inferred from the area of the Dirac impulse at 0 shift. Since we're in discrete-time, that would simply be the magnitude square of the 0 shift autocorrelation "sample", minus the sum of all powers in other shifts.

So, you do need to do a non-parametric spectrum estimate; you might want to look into classic periodograms (that's where your tag comes in!), but also into methods building on that, namely Welch's method.

Now, if you do have a noise model that says that your noise was formed in some specific way, and you using the term "colored noise" might indicate that, then you might actually have the chance to use a parametric estimator to get results of lower variance (or same variance with fewer samples). For example, if you assume your colored noise to be the result of white noise being filtered by some autoregressive system, then applying the Yule-Walker equations to estimate the autocovariance matrix of your noise would work! From the elements of that you can infer distribution of noise.

¹ exceptions: Noise's autocorrelation function is an Eigenfunction of the Fourier transform, scaled accordingly and the Fourier transform chosen is normalized to be unitary. I think that is unlikely here.

• Does detrend='constant' in scipy.signal.periodogram related to remove noise? Mar 15, 2022 at 18:10
• That is a very unrelated question. and no! Mar 15, 2022 at 23:18