Example 553

As a third and final example of the one-dimensional model for LI, consider a rectangular K(x) = ko for |x| 3 xo/2, and K(x) = 0 for |x| S xo/2. It is easily shown that K(u) = k^xo sin(uxo/2)/(uxo/2). Thus, L(u) = 1/[1 + K(u)] can be unstable (i.e., L(u) ^ x) if its first (negative) minimum ^ -1. To see at what value of its argument the first minimum of sin(x)/x occurs, one differentiates it and sets the derivative to zero.

FIGURE 5.3-8 The calculated spatial frequency response, L(u), of the linear, continuous, one-dimensional model of LI when the inhibition weighting function, k(x), is rectangular with width ±xo. Parameters: xo = 2, ko = 0.5, L(u) = 1/[1 + sin(u)/u]. See text for details.

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