Abstract: Fast Fourier Transform methods of analyzing signal frequencies spectra yield results from zero frequencies upwards. Thus, when the frequency band of interest is not at very low frequencies a lot of wasted calculations may be performed, and resolution and computation time have to be traded-off against each other, often falling short of the requirements for both. A technique is described in which the signal to be analyzed is passed through an anti-alias filter and initial transform data is collected by undersampling. In a railway track circuit receiver which is to identify a predetermined carrier frequency or FSK signal, the anti-alias filter is selected to exclude frequencies other than those in a frequency band including the particular track signal so that there is no ambiguity in the calculated transform results.