= Quadrature energy model of a complex cell
{title2=$E=(k_e*I)^2+(k_o*I)^2$}
Two oriented linear filters in quadrature have responses $A\cos\varphi$ and $A\sin\varphi$ to a suitably matched narrowband grating. Their squared sum is $A^2$, independent of phase $\varphi$, while orientation and spatial-frequency selectivity remain. A nonlinear output function or normalization can transform this energy into firing rate. Ideal quadrature gives an exact phase identity for the matched stimulus; finite approximate filter pairs need not have perfect invariance for arbitrary images.
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