How can I add gaussian noise in a specific percentage (e.g. add 5% gaussian noise to a signal)?

I have a regular signal in a vector, I want to add 5% gaussian noise to it, anyone got ideas? Thanks

[Image Analyst]

What is the 5%? Like every element has noise with a standard deviation of 5% of the element's value added to it? Or 5% of the elements have noise and 95% do not? Not to state the obvious, but have you looked at randn()?

[Pedro Alejandro Garza Juarez]

It's 5% uncorrelated Gaussian random noise.

[Image Analyst]

So, did my code below do what you want? If not, what do you want?

Answer 1

[Image Analyst]

Try this:

period = 20;
t = linspace(-20, 20, 500);
signal = 10*sin(2 * pi * t / period);
noiseSigma = 0.05 * signal;
noise = noiseSigma .* randn(1, length(signal));
noisySignal = signal + noise;
plot(t, noisySignal, 'r.', 'MarkerSize', 10);
hold on;
plot(t, signal, 'b-', 'LineWidth', 3);
grid on;

[Pedro Alejandro Garza Juarez]

Thank you!

[Darcy Cordell]

I have a question about your code. Your code is the "standard" way of adding noise. But I always am confused by it. When you say "5%" noise is added to the data, to me, this implies that the mean of the normalized residual is 5%. Is this a correct assumption?

m = mean(abs(signal - noisySignal)./abs(signal)); %To me, this should be equal to 0.05

However, in your case, m does not equal 5%. It consistently equals approximately 4%.

If I change the error level to 10%, then the mean of the normalized residual tends to be around 8%. For 20% noise, the mean of the normalized residual is around 17%.

Can you explain why this result occurs?

And, a broader question is: Given "signal" and "noisySignal", is there a way to recover the error percentage?

[Image Analyst]

You're using a different definition. I said that the standard deviation of the noise would be 5% of the signal amplitude at that point. I did not say the mean - that's a totally different definition.

[kasimala venkatanagaraju]

sir, I want to generate noise contaminated signal with zero mean and standard deviation of 2%. Can you help me how to generate it.

[Jubeyer Rahman]

Shouldn't be there be an sqrt before sigmanoise?