Detection of a known signal in colored Gaussian noise---A new coordinate approach (Corresp.)

The classical problem of detecting a known signal in additive colored Gaussian noise on a finite interval is considered by using as "coordinates" (observables) the inner products formed between the received waveform and the elements of a simply constructed complete set of functions defined on the observation interval. Results of the Karhunen-Loève (K-L) approach are thereby obtained without the K-L expansion or any appeal to results from integral equation theory.