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.