Exact discrete time synthesis

Abstract

A procedure for the exact synthesis of LDI ladder filters is developed. Starting from any realisable discrete-time z-plane transducer function H(z), irrespective of the s-z transformation used, a discrete-time loss-less passive ladder prototype is derived whose complex frequency variable is γ, the LDI variable, and whose terminations are resistive and functions of μ, where =(z 1/2 + z -l/2 )/2,γ =(z 1/2 - z -1/2 )/2 and z is the discrete-time complex frequency variable. The proposed synthesis procedure is carried out by introducing a discrete-time frequency transformation which maps the discrete-time z-plane into another discrete-time plane called the λ-plane, where λ = α + jβ. The discrete-time physical frequency variable s describes a straight line axis rather than a unit circle axis. The frequency characteristics of the synthesised discrete-time transducer function H(z) are exactly preserved in the discrete-time /lambda/-plane.