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This implies that data processing consists of a sequence of arithmetic operations. For example, if 10 numbers are to be added, 10 successive additions are performed. No additional equipment is needed if 100 additions are required instead. By contrast, an analog processor generally does not require a memory, which must be time-shared among the various mathematical operations. Rather, a separate electronic unit or ‘‘black box’’ is supplied for each mathematical operation. If a computation requires 10 additions, 10 analog operational units must be provided and interconnected; and all of these units operate simultaneously.

The transfer functions corresponding to the plots in (a) and (b) have the same magnitude characteristics but differ in phase characteristics. The transfer functions corresponding to the plots in (c) and (d) have the same phase characteristics but differ in magnitude characteristics. same, but the magnitude characteristics differ. Still, the second-order transfer function corresponding to Fig. 20(d) is a nonminimum phase one. Note that it has the same phase as the fourth-order transfer function corresponding to Fig.

Although IIR filters can be designed to approximate given magnitude and phase requirements, a popular approach to digital filter design is to base a design on continuous time filter approximations and transform the result to digital filter form. Then the phase is linearized (equalized) using cascaded digital all-pass filters. This approach is a practical one (among several practical approaches) if the order of the all-pass filter required is reasonable (28). To devise a first-order, real, stable, all-pass transfer function, we place a zero outside the unit circle in the z plane on the real axis at z = (1/r1 ) corresponding to a pole at z = r1 , |r1 | < 1.

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07.Circuits and Systems - Analog and Digital Signal Processing by John G. Webster (Editor)

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