COMPLEX-VALUED ADAPTIVE SIGNAL PROCESSING - Adaptive Signal Processing: Next Generation Solutions - page 49

Figure 1.9 (a) Magnitude, (b) phase, (c) real and (d) imaginary responses of the
split tanh function given in (1.43).

in the figures, though bounded, none of these functions can provide sufficient dis-
crimination ability, the split function in (1.43) shown in Figure 1.9 provides a
decoupled real and imaginary response while those shown in Figures 1.10 and 1.11,
provide smooth radially symmetric magnitude responses and a phase response that
is simply linear. The responses of the real and imaginary parts for these two functions
are the same as in the case for the split function. In [61-63] examples in system identi-
fication and channel equation are provided to show that these functions cannot use the

Figure 1.10 (a) Magnitude and (b) phase responses of the activation function given
in (1.44) for m ¼ 1.