FIGURE 5.3-5 (A) Diagram of three mutually inhibited eccentric cells from three separate ommatidia. The LI follows the form of Equation 5.3-2. (B) Light input stimuli vs. time for the three ommatidia. (C) Approximate instantaneous frequency vs. time for the three stimulated eccentric cells. Note that stimulation of adjacent ommatidia reduces the firing rate of the stimulated eccentric cell being recorded from.
Rather than work with a two-dimensional, discrete model using two-dimensional z-transforms, the properties of a continuous, linearized, one-dimensional, LI model using Fourier transforms will be examined. The discrete, one-dimensional, linearized LI model is r(x) = e(x) - J K(x - o) r(o) do
The summation term is interpreted as a one-dimensional discrete convolution of the inhibition weighting function, K(jAx) with the one-dimensional distribution of frequencies, r(jAx). To make the model continuous, assume that N ^ x, Ax ^ 0, and jAx ^ x, and pAx ^ ct in Equation 5.3-5. Thus, the discrete, finite LI model becomes r(x) = e(x) -1 K(x- o) r(o) do 5.3-6
When Equation 5.3-6 is Fourier transformed,
u is the spatial frequency in rad/mm. Collecting the terms, the transfer function is
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