# HOW CAN I CALCULATE THE SIGNAL TO NOISE RATIO(SNR) OF A CHIRP SIGNAL

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raj on 16 Apr 2012
I have a signal which is comprised of 4 chirp signals and an additive noise with the same sampling frequency and size is generated now i need to calculate the SNR of the signal and noise . Also if I am correct to vary the signal to noise ratio is it ok if I vary the amplitudes of chirp signals and also the noise by multiplying it with a factor : ex:
noise = randn(size(t));
where t = 0:1e-4:1;
and to increase the noise
{new noise = 2*noise ;}
is this correct?? and to increase the amplitudes of the signal is this the way to change the signal to noise ratio:
y3 = 5* chirp(t,600,t1,800,'linear');
​​​​​​​y4 = 3.5*chirp(t,900,t1,980,'linear');

Geoff on 7 Jul 2021
Edited: MathWorks Support Team on 7 Jul 2021
NR = Psignal / Pnoise = (Asignal / Anoise)^2
Where P is power, and A is amplitude. I would calculate the RMS amplitudes and use those in the above formula.
RMS means Root-Mean-Square. That is, you square your signal, calculate the mean of that, and take the square root. Just define a wee anonymous function for clarity:
RMS = @(x) sqrt(mean(x.^2));
Now you can compute your ratio like so:
RMS = @(x) sqrt(mean(x.^2));
Lesiba Amos on 28 Sep 2020
Lol why is the RMS(x)/RMS(n) squared?
Rohan Patni on 3 Oct 2020
Because power of a signal is directly proportonal to the square of the said RMS amplitude

Wayne King on 16 Apr 2012
You can increase the SNR by increasing the amplitude of the signal and by decreasing the variance of the noise. You have to remember that if you want to increase the variance of the noise by 2, you should multiply randn() by sqrt(2), not 2. Multiplying by two increases the variance by a factor of 4.
x = randn(100,1); % variance is 1
x = sqrt(2)*randn(100,1) % variance is 2
raj on 16 Apr 2012
how should i calculate SNR is it by calculating the variance of signal and noise and dividing them and then applyng log to it

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