Gaussian-response filter design

A resume of the magnitude, phase, impulse response, step response, and effective thermal noise bandwidth of perfect gaussian filters is given. A physically realizable approximation to the magnitude characteristic is then given. The complex frequency roots of this approximation (up to the 9th order) are supplied. Then considered, in order of synthesis complexity, is the use of these roots to design stagger-tuned systems, lossless and uniformly lossy filters resistively loaded on one end only, and the same filters resistively loaded on both ends; all designs supplying nth-order gaussian magnitude approximations. Numerical design data is supplied in 7 tables; a low-pass and a band-pass design example are given.