Generalized matched filtering

In digital matched filtering, a discrete-point input function is Fourier transformed to produce a discrete-point Fourier transform. This transform is then multiplied by the matched filter, the product is retransformed, and the resulting pattern is examined. It is shown that the problem of deriving the matched filter can be recognized as a special case of linear discriminant analysis, which in turn is a special case of principal component analysis. What linear discriminant functions are, and in what sense they are optimum, is described.