# Power Spectral Density of discrete White Gaussian Noise defined with variance and sampling interval

From Creighton and Anderson Chapter 7 on Gravitational Wave data analysis:

Please explain where the delta t and the limit came from in this derivation.

• I really don't think the right equality in $(7.22)$ makes much sense; $\lim\limits_{\Delta\! t\to 0}2\sigma^2\Delta\! t\equiv0$ for all finite $\sigma$. – Marcus Müller Jan 28 at 20:46
• But this result is needed in that text to derive the optimal matched filter used in GW data analysis, which they got right...this can be found in section 7.1.2 in the same text...are you sure that this is wrong. – Jyothis Chandran Jan 30 at 9:39
• yes, I'm sure. That's the definition of $\lim\limits_{\Delta t\to 0}\Delta t$. – Marcus Müller Jan 30 at 9:56