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

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');

Answer 1

[Geoff]

From Wikipedia: http://en.wikipedia.org/wiki/Signal-to-noise_ratio

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));

[raj]

for suppose there are 4 chirp signal and noise n

y1 = 12*chirp(t,100,t1,150,'linear');

y2 = 10*chirp(t,250,t1,350,'linear');

y3 = 5* chirp(t,600,t1,800,'linear');

y4 = 3*chirp(t,900,t1,980,'linear');

x = y1+ y2+y3 + y4;

how to calculate rms in matlab please explain

[Geoff]

I have edited my answer to include this information.

[raj]

should log be applied???

[Geoff]

This isn't really a MatLab question anymore. You might need to brush up on the theory of exactly what you are trying to do.

Like it says on that Wikipedia link I gave you that you surely have read, you take the log (base 10) if you want your SNR expressed in decibels.

So only you can answer the question of whether to apply log, because only you know whether you want the SNR in decibels or not.

x_snr_db = 20 * log10( RMS(x) / RMS(n) );

[raj]

thanks for ur help

[Geoff]

no worries =)

[Tahariet Sharon]

@Geoff: why "20"? in "20 * log10( RMS(x) / RMS(n) );"

[Seema Sud]

Note the square (^2). i.e. 10*log10(RMS(x)/RMS(n))^2

This is the same as 20*log10(RMS(x)/RMS(n)). No square here.

Rule of logarithms log(a^b) = b*log(a)

[Lesiba Amos]

Lol why is the RMS(x)/RMS(n) squared?

[Rohan Patni]

Because power of a signal is directly proportonal to the square of the said RMS amplitude

Answer 2

[Wayne King]

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]

how should i calculate SNR is it by calculating the variance of signal and noise and dividing them and then applyng log to it