Add random noise with specific SNR to a signal

Question

I have randomly generated signal for example:

%frequency
f1 = 1000; f2 = 2000;
Fs = 8000; %sampling frequency

%amplitudes
amp1 = 0.75;
amp2 = 0.2;

%time
dt = 1/Fs
stopTime = 0.3;
t = 0:dt:stopTime;

%random noise
noise = randn(1,length(t))

%generated signal
Signal = amp1*sin(2*pi*f1*t) + amp2*sin(2*pi*f1*t) + noise;

Now i need to create two Signals S1, S2 with random noise with specific SNR. Noise added to S1 must be uncorrelated with noise added to S2 Here is what i tried:

%SNR in dB
SNR = [-80,-40,-20,0,20,40,80];

%S1,S2 = Signal + rand noise with SNR -40dB
S1 = awgn(Signal,SNR(2),'measured')
S2 = awgn(Signal,SNR(2),'measured')

Is this correct approach to create random noise with SNR from range -80dB to +80dB? will noise added to S1 be uncorrelated with noise added to S2?

Answer 1

You could just calculate variance of signal and add noise with variance required to produce desired SNR. Here is some python code as an example

import scipy as sp
import scipy.fftpack as fft

# frequency
f1 = 1000.0
Fs = 8000.0  # sampling frequency

# amplitudes
amp1 = 0.75

# time
n = sp.arange(1024)

# Desired SNR in dB
SNR_dB = 40

# Desired linear SNR
snr = 10.0**(SNR_dB/10.0)
print "Linear snr = ", snr

# Measure power of signal
signal1 = amp1*sp.sin(2*sp.pi*f1/Fs*n)
p1 = signal1.var()
print "Power of signal1 = ", p1

# Calculate required noise power for desired SNR
n = p1/snr
print "Noise power = ", n
print "Calculated SNR =  %f dB" % (10*sp.log10(p1/n))

# Generate noise with calculated power
w = sp.sqrt(n)*sp.randn(1024)

# Add noise to signal
s1 = signal1 + w

will noise added to S1 be uncorrelated with noise added to S2?

Yes.