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An adaptive digital matched filter structure is developed for the case where the input signal is of known form and finite duration and the input noise has a power spectral density which is all-pole. The effect of noise spectrum identification errors on system performance is investigated both theoretically and experimentally. It is shown that, when the noise is highly correlated, the adapting structure leads to significant improvement in the output signal-to-noise ratio (and hence in the detection characteristics) with relatively short measurement times. This suggests the use of switching logic to allow noise adaptation only when measurements indicate a highly correlated noise background.