# Gravitational wave data analysis. More of Signal processing techniques

## Main Question or Discussion Point

I am using the matched filtering technique to extract the data from a heavy noise background in the process of detection of gravitational waves. I calculate the correlation between the experimental data and a theoretical template.
I have been told that the maximum of the correlation function will be the signal to noise ratio. Just for confirming this, I just took an example.
I generated a sine function (pure sine wave), and then added gaussian white noise(mean=0, variance=1) to it. Now I cross-correlate these two, ie pure sine wave and sine wave added with noise. I used the correlation theorm to calculate it, ie doing an fft and taking the ifft of it. I find that the maximum value turns out to be somewhere between 40 and 65.
Now for checking whether that is the true snr, I tried calculating the snr as
snr=(Amplitude of Signal/ Amplitude of noise)^2;
I calculated the amplitude as the rms value in both the cases(signal and noise). The answer always turned out to be somewhere between 0.38 and 0.65 or around. I am not able to understand my mistake and whether I am correct in checking the snr like this.
For further clarification, I did the same thing with a gaussian signal, and found a similar problem. Can any one please tell me, where am I going wrong???

## Answers and Replies

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Stephen Tashi
Science Advisor
then added gaussian white noise(mean=0, variance=1) to it.
Did you generate the values of the process at discrete time intervals? Did the gaussian random variable you used at each interval have variance = 1? If so, shouldn't you have made it smaller?

I am using octave for my analysis. What I did was, I defined time variable t from 0 to 10 in steps 0.1. then generated gaussian random values of the same length(101) using the randn function, which gives gaussian random numbers with mean=0 and variance=1 by default. are u saying, i shud make the variance smaller? how is that going to help? and am I following the correct procedure of calculating the snr?
Thank you very much for your reply.

Stephen Tashi
Science Advisor
I defined time variable t from 0 to 10 in steps 0.1. then generated gaussian random values of the same length(101) using the randn function, which gives gaussian random numbers with mean=0 and variance=1 by default. are u saying, i shud make the variance smaller? how is that going to help?
I don't know how it will help but it can't hurt to straighten this point out. I'm not a signal processing guy and I'm looking at what you're doing from the point of view of probability theory. You say that the Gaussian noise has "amplitude 1". What does that mean to you? From the point of view of a stochastic process, the variability of a continuous process based on a Gaussian distribution is isn't determined by the standard deviation of a Gaussian distribution independently of how often (in time) you make a random draw from that that distribution. If you had drawn random values from Gaussian distribution with standard deviation 1 every .001 seconds, you would have a process that is more variable than the process you got by drawing from that distribution every 0.1 seconds. If "amplitude" is to make sense the formula for calculating it must have a "per unit time" consideration in it.

What is the definition of the "amplitude" of Gaussian noise in signal processing? (This isn't a hint, because I really don't know.) When you have a data sample, what calculation do you do to estimate its amplitude?

and am I following the correct procedure of calculating the snr?
Not being a signal processing guy, I can't tell you. If we settle on how to calculate the amplitude of Gaussian noise, then we'll worry about that.