# If add white noise to the signal, how much does the std of the noise affect the thd of the signal?

I'm an electrical department student studying signals and systems.

The RMS value of the general AC electrical signal is 6.31V, and the first harmonic value is 6.30932V(rms). (THD is approximately 1.5% at this time.)

How much does the std value of the white noise added to the signal affect the THD value of the signal?

When tested in the simulation, thd became 2.8 to 3% when the std value of white noise was 0.16. However, in the fft distribution of white noise, it was too complicated to calculate because the value of the harmonics was very small, such as 0.015, or a minus value.

When white noise is added to the signal, how should the THD value calculation expression be constructed?

(THD is approximately 1.5% at this time.)

How did you calculate that ? Given your numbers I would expect your to be THD+Noise to be about 7% . Do you have both harmonic distortion and noise in your signal ?

When white noise is added to the signal, how should the THD value calculation expression be constructed?

That's actually a complicated question. THD, as the name implies, quantifies "harmonic" distortion, i.e. noise at specific discrete frequencies. White noise is broad band and the spectral density at each individual frequency is actually zero. So paradoxically adding white noise, does NOT change the THD. To capture both noise mechanisms many people use THD+Noise instead.

In practice you will always have to use a finite analysis window and a finite spectral resolution, so you will see the THD increasing somewhat, but the amount will depend on the analysis parameters. For example, the longer the FFT, the less the THD will be affected (assuming you don't have spectral leakage).

• Sorry ...1st harmonic rms value is 6.30932V. yes i use FFT analysis 20 dimension. Commented Oct 25, 2022 at 13:58
• FFT analysis for THD is fairly complicated and you have to get all the details right. How do you know your current measurements are correct? Did you do unit tests with known signals and answers ? Commented Oct 25, 2022 at 15:44
• I think Hilmar's point needs stressing: White noise does not increase the THD. It increases the error that a non-perfect estimator for the THD would do. And that's what you see. Your THD stays the same, but your way of calculating it becomes more and more wrong. Commented Oct 25, 2022 at 15:44
• Thank you very much for your reply! Commented Oct 26, 2022 at 2:47