How to add white gaussian noise with variance 1 to a signal and calculate the signal-to-noise ratio?

Hi. I have a signal that I want to add white gaussian noise to. The variance of the white gaussian noise is 1. Then I will pass it to a low pass filter. Hence, I want to find out the signal-to-noise ratio at both input and output.

After some googling, I understand that I need to use awgn or wgn to add white gaussian noise to the signal. However, I'm getting quite confused with awgn which takes in the signal and signal-to-noise ratio and for wgn, which takes in the M-by-N matrix and power of the noise in dB. I do not have any of the variables and only know that the variance of the white gaussian noise should be 1. Does anyone know how I can add white gaussian noise to the signal? I think I might need to use randn but is not very sure how I can use it.

Can someone help me out?

Answer 1

[Wayne King]

Just use randn()

   t = 0:0.001:1;
   x = cos(2*pi*100*t)+randn(size(t));

To use a different variance, multiply randn() by the square root of the variance

For example, for a variance of 2

   noisevec = sqrt(2)*randn(1000,1);

[Sakura]

What does randn(size(t)) means?

[Wayne King]

It means a vector the size of the time vector. When you add two vectors, they must be the same size (not just same length). Since I'm forming a cosine by using t, randn(size(t)) gives me a noise vector of the same size. You could of course do something like:

   t = 0:0.001:1;
   sig = cos(2*pi*100*t);
   noisevec = randn(size(sig));
   sigplusnoise = sig+noisevec;

[Sakura]

Oh I see. So sigplusnoise will be signal and white gaussian noise with variance 1?

[Wayne King]

yes.

[MAHESH MOHAN]

Hello I've seen somewhere,in which apart multiplying from std deviation of noise signal,also divided it by std deviation of randn function.Could u say the notion behind this..is it some sort of normalization

noise = randn(nRow, nCol); i1 = i+sigma*noise/std2(noise); imshow(i1,[0,255]);title('ORIGINAL IMAGE');

where i is the original image and nrow and ncol its dimensions. Thanku for ur time Mahesh Mohan.M.R