How to add a white Noise with rms amplitude of 0.5 v by matlab?

Write an m-file with MATLAB, define a signal with an amplitude of 0.7 V at 20 Hz and an amplitude of 1 V at 50 Hz. Now run a frequency analysis following settings respectively: a) Sampling rate: 1000 Hz, signal length: 1 s b) Same with a) but add white noise of rms-amplitude of 0.5 V

I am confused with (b). How can I solve it ?

Answer 1

[Star Strider]

The randn function returns normally-distributed random numbers with a mean of 0 and a standard deviation of 1. The standard deviation is essentially the rms value. So multiply your randn vector by 0.5.

[Chung Di]

Could u please write the command, it will be helpful. Thank you

[Star Strider]

Your signal is sampled at 1000 Hz (sampling frequency) and is 1 second long. So you need to tell randn to return a vector of 1000 samples that is the same row and column size as your signal vector, then multiply that noise vector by 0.5 before adding it to your signal vector.

If ‘s’ is your signal vector, your noise vector would be

nv = 0.5*randn(size(s));

See the documentation on randn (link) for details.