Signal to noise ratio definition

The current text is this:

the square root of the integral over frequency of the power spectral density of the gravitational-wave signal divided by the integral over frequency of the average power spectral density of the noise

I doubt that anyone could use this verbal description to write the correct equation (.. what is inside or outside the square root?) - plus I don't think the description is necessarily valid for all relevant contexts; for matched filter SNR (squared) you divide the signal squared by the noise PSD and there is only one integral.