Difference between randn() and awgn() in adding white noise to a signal

Hi everyone

I'm trying to add a white noise to my signal and simulate it for different SNR values.

But I'm not sure if i should use randn() or awgn().

For instance I don't understand why these two methods deliver different signals in my code.

t=linspace(0,120,8000);      
x=sin(2*pi*0.01.*t+pi/3).*cos(2*pi*0.01.*t+pi/3);    %Original signal
 
n=2*randn(size(x));  %white noise

xn=x+n;                      %noisy signal method 1
SNR=snr(xn,n);
x2=awgn(x,SNR,'measured');   %noisy signal method 2

subplot(2,1,1);plot(t,xn);      
title('Signal with white noise using randn');
subplot(2,1,2);plot(t,x2);
title('Signal with white noise using awgn');

I'd be very grateful for your clarifications and suggestions!

[Walter Roberson]

With that option to awgn, the multiplier for randn() is sqrt(10^(SNR/10)) .

Your original multiplier was 2.

In order for those to match, SNR would have had to have been log10(2^20) or about 6.02 but it is about 0.12

Question: are you sure you want to measure SNR of xn (noisy x) against n (noise), instead of measuring SNR of xn (noisy x) against x ?

[bob98]

Thank you for your answer, but i'm not sure what you mean by multiplier,standard deviation ? (sorry but i'm still an absolute beginner in Matlab..)

otherwise regarding your question, this is how the SNR of xn is defined, right ? noisy signal/ noise ??

Answer 1

[Shubham Rawat]

Hi bob,

Here in xn the noise you are adding is

n = 2*randn(size(x)); % noise using multiplier 2
xn = x + n;

Whereas in x2,

SNR=snr(xn,n);
x2=awgn(x,SNR,'measured'); % noise using multiplier sqrt(10^(SNR/10)) 

[bob98]

Thank you for your clarification.

So as far as i understand we have here 2 different variance values 1st one is 4 the 2nd one is 10^(SNR/10).

So how does that influence the snr values (signal,noise) especially as the second one is given as input?

How do i get both methods to generate signals with the same SNR?

I look forward for your answer.

Answer 2

[Paul]

This seems to get closer to what you're expecting:

t = linspace(0,120,8000);

x = sin(2*pi*0.01.*t+pi/3).*cos(2*pi*0.01.*t+pi/3); % Original signal

S = RandStream.getGlobalStream;

S.reset;
noise = 2*randn(size(x));
xn1 = x + noise;

S.reset;
SNR = snr(x,noise); % use the nominal signal
xn2 = awgn(x,SNR,'measured');

max(abs(xn1-xn2))

ans =

   4.8495e-02

I was hoping that xn1 == xn2. They are close, but not quite equivalent.