On the response and approximation of Gaussian filters

This paper discusses a filter whose amplitude response characteristic is
e^{k\gamma^{2}}
where γ is a function of frequency and k is a constant related to the filter bandwidth. The amplitude response curve of this filter has the shape of the Gaussian probability function and it is shown that the phase response curve may be assumed to be linear. Previous investigators have shown that such a filter has excellent transient characteristics and that in some sense, it is the optimum filter for transient signals. The responses to impulse and step functions are discussed in this paper. A method for designing an approximate Gaussian filter is given, and the measured responses of such an approximate Gaussian filter are presented.