Mapping from the s-domain to the z-domain via the phase-invariance method

There are several methods in the literature for mapping from an s plane to a z plane. The two most common methods are the impulse-invariance method and the bilinear transform. In this paper, an algorithmic method is presented such that phase characteristics on the jωjω omega axis in the s plane are preserved on the unit circle in the z plane. This preservation of the phase is not accomplished with other methods. As a useful example in this paper, the algorithm is applied to the design of linear phase Bessel IIR digital filters. This new method is denoted as the phase-invariance method (PIM) and is a modification of the magnitude-invariance method (MIM). The mapping is not restricted to lowpass or bandpass analog prototype transfer functions.