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A nonminimum phase transfer function can be expressed as the product of a minimum phase transfer function and an all-pass transfer function. For example, suppose we have the transfer function T (s) = (s − 1)[(s − 3)2 + 1] [(s + 1)2 + 1][(s + 2)2 + 1] By multiplying T(s) by and regrouping the factors, we obtain where TMP (s) is a minimum phase transfer function and TAP (s) denotes an all-pass transfer function. For sinusoidal steady state analysis applications, a minimum phase transfer function T(s) can be expressed in the form where α(ω) is the attenuation function in nepers and θ(ω) is the negative of the phase function in radians.

In most system analyses, time and space constitute the independent variables. That is, measurements are distinguished from each other and ordered according to the location in the time–space continuum at which the measurements were made. The measured quantities are the dependent variables, and they may be expressed as functions of time and/or space. Some familiar dependent variables include voltage, displacement, velocity, pressure, temperature, stress, and force. The measurement of these variables requires the selection of appropriate instruments, along with a decision as to the manner in which the measurements are to be recorded and utilized.

39), it is seen that ZA = 1 and the box labeled ZB in Fig. 14 consists of the series connection of a 1 Henry inductor and an LC tank circuit that resonates at 1 rad/s. However, the resulting circuit requires six reactive elements and does not have a common ground between the input and output ports, and these properties may preclude the use of bridge circuit allpass networks in some applications. Single transistor first-order all-pass transfer function realizations have been described by several authors.

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