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

In this paper, a new mapping between the s-domain and the z-domain is reported. This method is denoted as the magnitude-invariance method (MIM). Under this mapping, it is shown that the autocorrelation function of the unit sample response of the discrete-time system is samples of the autocorrelation function of the Dirac impulse response of the analog prototype convolved with a sine function. If the magnitude frequency response for the analog prototype, for normalized radian frequencies, is strictly bandlimited to less than \pi\, then MIM is equivalent to autocorrelation-invariance; The new method (MIM) is unique in that it produces a magnitude frequency response of the discrete-time rational transfer function that exactly (theoretically) follows that of the analog prototype rational transfer function for normalized radian frequencies from -pi to pi, unlike that of any other mapping from the s-domain to the z-domain, including the impulse-invariance and bilinear transform methods. In some applications this may be advantageous, such as in routine digital filter design based on an analog prototype, analog magnitude frequency response equalization via a digital filter, etc. This mapping is not restricted to lowpass or bandpass analog prototype transfer functions. (C) 1998 Elsevier Science B.V. All rights reserved.