Superimposing x% RMS noise to a signal

Question

상훈 송 2022-12-22

回答： Mathieu NOE 2022-12-23

Hello, I hava a question about superimposing certain percent of RMS noises to a signal (for example 2% RMS noises).

First of all, I not sure about the percent. Is percent refers that my signal and the superimposed noise has a 2% RMS value?

Second, implementing it at MATLAB.. my signal has a size of 10001 x 3.

Best regard

Answer 1

Mathieu NOE 2022-12-23

hello

the logic would be to add x % of rms noise to the rms amplitude of your clean signal

so compute the rms value of each column of your signal , multiply by x/100 *randn(10001 ,1) (and repeat for the others columns)

NB : randn generates a rms = 1 noise (it get's closer to 1 as the number of samples increases)

x = randn(10001,1);
x_rms = sqrt(mean(x.^2))

x_rms = 1.0067