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The authors present a new Fourier transform theory which provides analytic results for both strongly coupled fiber Bragg grating and photonic crystal filter structures. Trigonometric and hyperbolic descriptions of these important passive optical devices are well known for the regular grating case. However, the unified approach presented here, which is based upon a modified Debye-Waller approach to the analytical solution of the coupled-mode equations, allows intuitive, yet accurate appraisal of arbitrary-strength-coupled structures. It is also applicable to perturbed-periodic gratings, such as linearly chirped devices for dispersion compensation.