From this relation, it is evident that the argument for the first minimum occurs when x = tan(x). Solution of x = tan(x) occurs for x = 4.49341 rad, or 257.45°. Substituting this value back into sin(x)/x gives the first minimum = -0.217234. So ko < 1.6116/xo for LI system stability. The first peak in the frequency response, L(u), occurs for uxo/2 = 4.49341, or u = 8.9868/xo. Figure 5.3-8 illustrates the frequency response, L(u), of the LI system. Note that the ripples die out to a steady-state, high-frequency level of L = 1, and L(0) = 1/(1 + koxo).
There is much evidence that LI occurs in certain vertebrate visual systems. Neurophysiological evidence taken from the ganglion cells (optic nerve fibers) of the eyes of cats, frogs, pigeons, etc. indicates that basic high-pass spatial filtering takes place in vertebrate retinas before high-frequency cutoff. As has been seen, spatial high-pass filtering enhances contrasting edges. Other "operations" on visual information, called feature extraction, also take place at the retinal level in vertebrate eyes (Lettvin et al., 1959), as well as in insect OLs. Feature extraction is described in detail in Section 5.4. Indirect evidence for LI can also be taken from psychophys-ical studies of human visual perception. Our visual system definitely sharpens h 0 30 -10 30
contrasting boundaries. For example, stare at a sheet of paper, half-white, half-black. At the white/black boundary, people perceive the white whiter, and the black blacker. In some cases, it is even possible to see one or two bands at the boundary, illustrating an underdamped spatial frequency response of L(u).
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