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## 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???

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???