then the spatial tuning of the P cell is the Fourier transform ( F[P]) of Equation 3. F1/2Prþg/C0/C138¼0:5ð Rþ GÞa2f2 s Hsðfs Þ(Achromatic tuning) þð R/C0GÞH1:83sðfs Þ(Chromatic tuning) ð5Þ where Hs(fs) is exp[ /C02(psfs)2] (the Fourier transform of the center Gaussian), a=2p, and fsis spatial frequency. The achromatic term is a spatial bandpassfilter; the chromatic term is lowpass, multiplexing thechromatic and achromatic information into different frequency ranges. If the multiplexing filters had no overlap, two well-chosen cortical filters could perfectlyseparate (demultiplex) the chromatic and achromaticinformation (Kingdom & Mullen, 1995; Billock, 1991,1995). For P cells, the encoding filters overlap, inducingcrosstalk in the cortical decoders, especially at moderatespatial frequencies where the overlap is greatest. Consider the extraction of achromatic information from P cells by the simplest spatial bandpass filter—spatial differentiation (Billock, 1995). Taking the nth local derivative of the P-cell array is equivalent to differ-entiating Equations 3 or 5, with respect to a spatialdimension; in neural terms it corresponds to buildingcortical dual-opponent cells (Thorell, De Valois, &Albrecht, 1984) by lateral inhibition between afferentgeniculate cells (for details, see Billock, 1995). In the spatial domain, such derivative operators look like simple cells; 1-D differentiation produces oriented cellsand the order of differentiation determines the numberof alternating excitatory and inhibitory lobes; Equation 6describes a cell that has n+ 3 receptive field lobes when probed with achromatic spots, but n+ 1 lobes for equiluminant hue probes. The spatial frequency re-sponse ( A(f s)) of such an achromatic mechanism to a stimulus (defined in terms of L-and M-cone absorp-tions) Z(fs)={ R(fs),G(fs)} is Aðfs Þ¼Zðfs Þð F1/2Dn Pðfs Þ/C138Þ ¼0. 5[R(fs)+G(fs)]anþ2fnþ2 s HS(fs) (achromatic response) þ1/2Rðfs Þ/C0Gðfs Þ/C138anfn s H1:83sðfs Þ (chromatic crosstalk)ð6Þ This bandpass filtering model correctly predicts the spatial tuning of cortical cells sensitive to both achro-matic and chromatic contrast (but presumably labeledonly for achromatic contrast; Billock, 1995). Increasingnshifts the tuning to higher spatial frequencies and narrower bandwidths. The typical cortical cell has anachromatic bandwidth of 1. 4 octaves (De Valois & De Valois, 1988) matching the achromatic term of Equation 6 if n= 2 (i. e., matched filtering for lumi-nance signals in P cells). Similarly, color signals can beextracted by matched lowpass filtering (second-order integration), resulting in achromatic crosstalk at all butthe lowest spatial frequencies. Cðfs Þ¼Zðfs Þð F1/2D/C02Pðfs Þ/C138Þ ¼0:51/2Rðfs Þþ Gðfs Þ/C138H1:83sðfs Þ (luminance crosstalk) þ[R(fs)--G(fs)]H3:35s(fs) (chromatic response) An engineer would find this odd—this kind of cross-talk is generally undesired and avoided in communica-tions systems. Yet, as discussed below, crosstalk is useful information for binding. Estimation of Stimulus-induced Correlations between Spatial and Chromatic Mechanisms The discussion of crosstalk above was deliberately over-simplified to illustrate general principles. To estimatecrosstalk-based correlations, we generalize Equations 6and 7, to include the temporal response. Selective two-dimensional ( x,t) spatio-temporal matched filtering of Equation 2 yields Aðfs;ft Þ¼[R(fs,ft)+G(fs,ft)][Se(fs)Te(ft)--Si(fs)Ti(ft)]2 f Achromatic response g þ1/2Rðfs;ft Þ/C0Gðfs;ft Þ/C1381/2Seðfs ÞTeðft Þ þ Siðfs ÞTiðft Þ/C1381/2Seðfs ÞTeðft Þ/C0Siðfs ÞTiðft Þ/C138 f Chromatic Crosstalk g Cðfx;ft Þ¼[R(fs,ft)--G(fs,ft)][Se(fs)Te(ft)+Si(fs)Ti(ft)]2 f Chromatic Response g þ1/2Rðfs;ft Þþ Gðfs;ft Þ/C1381/2Seðfs ÞTeðft Þ þ Siðfs ÞTiðft Þ/C1381/2Seðfs ÞTeðft Þ/C0Siðfs ÞTiðft Þ/C138 f Achromatic Crosstalk g Although not as elegant as Equations 6 and 7, Equa-tions 8 and 9 are computable if the Se,Si,Te,Tifunctions can be estimated (see Kelly, 1989; Burbeck & Kelly,1980; for methods and estimated functions). We could use Equations 8 and 9 as INPUT 1, INPUT 2in Equation 1 and ignore Q1,2; the correlated input is implicit. Howev-er, it is enlightening to use only the achromatic andchromatic response terms (the terms in bold type) as INPUT 1, INPUT 2and to use Equations 8 and 9 (with the crosstalk terms) to estimate the stimulus-driven correla-tions ( Q 1,2in Equation 1) between spatial mechanisms that extract information from P cells about achromatic form and other mechanisms that extract information about color or chromatic form. We define spectralcorrelation as the integrated overlap of the Fourierspectra of two functions (an analog of Signal Detection(7) (8) (9) Billock and Tsou 1039