Optimum Phase Equalization of Filters for Digital Signals

Digital information transmitted by means of a pulse amplitude modulation scheme depends critically on the pulse shape for reliable high speed communications. The pulse shape, in turn, depends in great measure on precise phase equalization. A new technique for the design of phase equalizers, based on digital mean square error, has been developed. This criterion is appropriate for a digital transmission system because it can be related to the system error rate. A lower bound to the digital mean square error is first obtained by determining the theoretically optimum phase. A physical equalizer consists of a cascade of many (say N) constant resistance all-pass networks. For each nf several different values of N, an optimization search over the parameters of the all-pass networks is then done. The smallest value of N which yields an error satisfactorily close to the lower bound is utilized for the optimum physical phase equalizer. The major benefits derived from using this technique as opposed to the conventional one are: (i) A significant reduction in the number of all pass sections required. (ii) More practical element values, facilitating network manufacture. (in) A substantial improvement in system performance. I. INTRODUCTION' Most information transmitted via telephone facilities today is sent over analog channels. It is anticipated, however, that future systems will be largely digital. New services such as Picturephone will be transmitted over toll facilities in a digital format.