Conventional plane wave array theory does not apply to arrays in an inhomogeneous medium. In a stratified waveguide such as the ocean there are many modes of propagation, and each of them is dispersive. As expressed in normal mode formalism, the transmission between vertical arrays can be considered as a filter problem. In this paper we consider the response of the array filters to an ambient noise field, and maximize the signal-to-noise ratio for transmission in a noisy waveguide. The resulting optimum, or matched array, filter is given by the conjugate of the product of the source function and the waveguide transmission function. The response of the matched array filter is weighted with the reciprocal of the noise power in each mode and the attenuation.

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