A detection scheme is developed under the assumption that a true target‐generated acoustic signal is accompanied by a weak frequency‐shifted replica. Our analysis shows that the correlation between the signal and its corresponding frequency‐shifted replica is the decisive factor. Optimum filtering techniques and performance measures are discussed. In the cases where the signal spectrum and the spectra of its replicas are overlapping, it is found that the performance will decrease with increase of overlap. Depending on the shape of the spectra, such degradation may be drastic.