On Using Gaussian Filter Characteristics for Approximate Autocorrelation Calculations
Haim Goldman · IRE Transactions on Communications Systems · 1966
\parallel R_{yy} (\tau) \parallelcalculations for two circuits (one of whose amplitude characteristic approaches the other as a limit) show that convergence of one type (filter amplitude convergence) does not imply smooth convergence of the circuit's output autocorrelation function. Specifically, the autocorrelation function of a cascade of amplifiers does not behave uniformly (or expectedly) as the number of stages increases. For the same bandwidth, the output autocorrelation function of a Gaussian filter matches best for small numbers of cascaded stages (and small τ).