The application of prolate spheroidal wave functions to the detection and estimation of band-limited signals

A solution to the detection Fredholm equation for band-limited noise and signal is presented which makes use of the dual orthogonality and completeness of the prolate spheroidal wave functions. Although data are available only on a finite interval, the detector in principle achieves the same optimum performance as if the interval were infinite. This apparent anomaly is resolved in an example.