Chebyshev All-Pass Approximants for Time-Delay Simulation

This paper presents tables of all-pass rational transfer functions that approximate a time delay τ to within an error ϵ for frequencies ω such that 0≤ωτ≤k. The coefficients are optimized to maximize the bandwidth k, if the order n of the transfer function and the maximum error ϵ are predetermined by the user. Two sets of tables are given, corresponding to two different error criteria: 1) ϵ = max |ϵT|, where ϵT(ω73x003C4;) represents a relative delay time error (100 ϵT is the percent error of the time delay) 2) ϵ = max |ϵ
_ø
|, where ϵ
_ø
(ωτ) represents a phase shift error. The tables are presented for discrete ϵ. A proof that the coefficients maximize the bandwidth and a description of the digital computer program used to obtain the tables are also given.