Chebyshev All-Pass Approximants for Time-Delay Simulation

This paper presents tables of all-pass rational transfer functions that approximate a time delay ¿ to within an error ¿ for frequencies ¿ such that 0¿¿¿¿¿. The coefficients are optimized to maximize the bandwidth ¿, if the order n of the transfer function and the maximum error ¿ are predetermined by the user. Two sets of tables are given, corresponding to two different error criteria: 1) ¿ = max |¿T|, where ¿T(¿¿) represents a relative delay time error (100 ¿T is the percent error of the time delay) 2) ¿ = max |¿¿|, where ¿¿(¿¿) represents a phase shift error. The tables are presented for discrete ¿. A proof that the coefficients maximize the bandwidth and a description of the digital computer program used to obtain the tables are also given.