How do I add gaussian noise with mean=0 and var=0.5 to a signal?

I need to add a gaussian noise that has mean=0 and var=0.5 to a signal. The code i tried is below

F0=30;
T=0:0.01:4.99;
std= sqrt(0.5);
noise = std.*randn(length(T),1);
S=sin(2*pi*F0*T)+noise;
plot(T,S)

For some reason the plot is strange. Can anybody see where the mistake is?

Answer 1

[Star Strider]

F0=30;
T=0:0.01:4.99;
std= sqrt(0.5);
noise = std.*randn(length(T),1);
S=sin(2*pi*F0*T)+noise                                          % 'noise' Is A Column Vector Here

S = 500×500

1.1726 2.1236 0.5848 0.5848 2.1236 1.1726 0.2215 1.7604 1.7604 0.2215 1.1726 2.1236 0.5848 0.5848 2.1236 1.1726 0.2215 1.7604 1.7604 0.2215 1.1726 2.1236 0.5848 0.5848 2.1236 1.1726 0.2215 1.7604 1.7604 0.2215 0.7899 1.7409 0.2021 0.2021 1.7409 0.7899 -0.1612 1.3776 1.3776 -0.1612 0.7899 1.7409 0.2021 0.2021 1.7409 0.7899 -0.1612 1.3776 1.3776 -0.1612 0.7899 1.7409 0.2021 0.2021 1.7409 0.7899 -0.1612 1.3776 1.3776 -0.1612 -0.3697 0.5813 -0.9575 -0.9575 0.5813 -0.3697 -1.3208 0.2181 0.2181 -1.3208 -0.3697 0.5813 -0.9575 -0.9575 0.5813 -0.3697 -1.3208 0.2181 0.2181 -1.3208 -0.3697 0.5813 -0.9575 -0.9575 0.5813 -0.3697 -1.3208 0.2181 0.2181 -1.3208 0.3447 1.2957 -0.2431 -0.2431 1.2957 0.3447 -0.6064 0.9324 0.9324 -0.6064 0.3447 1.2957 -0.2431 -0.2431 1.2957 0.3447 -0.6064 0.9324 0.9324 -0.6064 0.3447 1.2957 -0.2431 -0.2431 1.2957 0.3447 -0.6064 0.9324 0.9324 -0.6064 0.1462 1.0973 -0.4416 -0.4416 1.0973 0.1462 -0.8049 0.7340 0.7340 -0.8049 0.1462 1.0973 -0.4416 -0.4416 1.0973 0.1462 -0.8049 0.7340 0.7340 -0.8049 0.1462 1.0973 -0.4416 -0.4416 1.0973 0.1462 -0.8049 0.7340 0.7340 -0.8049 0.5132 1.4643 -0.0745 -0.0745 1.4643 0.5132 -0.4378 1.1010 1.1010 -0.4378 0.5132 1.4643 -0.0745 -0.0745 1.4643 0.5132 -0.4378 1.1010 1.1010 -0.4378 0.5132 1.4643 -0.0745 -0.0745 1.4643 0.5132 -0.4378 1.1010 1.1010 -0.4378 -0.1112 0.8398 -0.6990 -0.6990 0.8398 -0.1112 -1.0623 0.4765 0.4765 -1.0623 -0.1112 0.8398 -0.6990 -0.6990 0.8398 -0.1112 -1.0623 0.4765 0.4765 -1.0623 -0.1112 0.8398 -0.6990 -0.6990 0.8398 -0.1112 -1.0623 0.4765 0.4765 -1.0623 -1.3518 -0.4008 -1.9396 -1.9396 -0.4008 -1.3518 -2.3029 -0.7641 -0.7641 -2.3029 -1.3518 -0.4008 -1.9396 -1.9396 -0.4008 -1.3518 -2.3029 -0.7641 -0.7641 -2.3029 -1.3518 -0.4008 -1.9396 -1.9396 -0.4008 -1.3518 -2.3029 -0.7641 -0.7641 -2.3029 -0.7223 0.2288 -1.3100 -1.3100 0.2288 -0.7223 -1.6733 -0.1345 -0.1345 -1.6733 -0.7223 0.2288 -1.3100 -1.3100 0.2288 -0.7223 -1.6733 -0.1345 -0.1345 -1.6733 -0.7223 0.2288 -1.3100 -1.3100 0.2288 -0.7223 -1.6733 -0.1345 -0.1345 -1.6733 -0.6051 0.3459 -1.1929 -1.1929 0.3459 -0.6051 -1.5562 -0.0173 -0.0173 -1.5562 -0.6051 0.3459 -1.1929 -1.1929 0.3459 -0.6051 -1.5562 -0.0173 -0.0173 -1.5562 -0.6051 0.3459 -1.1929 -1.1929 0.3459 -0.6051 -1.5562 -0.0173 -0.0173 -1.5562

figure
plot(T,S)

It appears tto be strange because ‘S’ created a matrix, not the vector you were likely expecting. Beginning with R2016b, MATLAB has used ‘autoomatic explicit expansion’ so adding a row vector (‘sin(2*pi*F0*T)’) to the ‘noise’ column vector created the matrix. (In previous versions, this would have thrown an error.)

If you create ‘noise’ as a row vector, the result is:

S=sin(2*pi*F0*T)+noise.'                                        % 'noise' Is A Row Vector Here

S = 1×500

1.1726 1.7409 -0.9575 -0.2431 1.0973 0.5132 -1.0623 -0.7641 -0.1345 -1.5562 -0.0169 1.6593 -0.1544 -0.1968 -0.1232 -1.0387 -1.7588 0.4420 0.3897 -1.5253 0.6627 -0.1768 -0.3381 -1.0705 1.4712 0.6104 -1.9627 1.4861 0.4253 -0.0269

figure
plot(T,S)

.

[Matteo Svaldi]

Thank you very much, I appreciate your help

[Star Strider]

As always, my pleasure!