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A realizable, low-pass, minimum-phase transfer function is constructed which produces "maximally flat" time delay as a function of frequency, and which is associated with an impulse response that resembles closely a Gaussian curve properly delayed with respect to t= 0. The delay and loss characteristics are particularly easy to evaluate, since this transfer function can be expressed in terms of conveniently tabulated functions. It is shown how to realize this transfer function as the transfer impedance of a ladder network containing only low-Q elements, and the response of this network is put into perspective to those of conventionally designed delay networks. Also, a class of nonminimum-phase transfer functions is generated from the above transfer functions in order to offer added flexibility. The delay and loss characteristics of the nonminimum-phase transfer functions are described, but their network realization is not considered in this paper.