add (white) Gaussian noise to displacement signal, noise level = ( |x-x*| / |x*| ): can I use utilize awgn()?

I want to add artificial (white) Gaussian noise to my numerically generated signal. In the title of my question,

x %is the displacement signal including noise
x* %is the noiseless displacement signal
noise_level = ( |x-x*| / |x*| )

I read that awgn() function requires the signal-noise-ratio. I have no deep knowledge about signal theory.

My question is whether I can translate my noise_level into a SNR?

Answer 1

[Nadia Shaik]

Hi Simon,

I understand that you want to translate noise level to SNR so that you can add AWGN noise to a signal.

SNR stands for Signal-to-Noise Ratio, which is a measure of the ratio of the power of the signal to the power of the noise. It is often expressed in decibels (dB) and is a common metric used to evaluate the quality of a signal in the presence of noise.

The formula to convert noise_level to SNR in decibels (dB) is:

SNRdB = 10 * log10(P_signal / P_noise)

where P_signal is the power of the noiseless signal, and P_noise is the power of the noise.

To calculate P_noise, you can use the following formula:

P_noise = (noise_level * norm(x))^2;

where x is the noiseless signal.

You can calculate SNR and then pass it to "awgn" function to add Gaussian noise to your signal.

I hope this helps!