Multiple frequency detection in undersampled waveforms

The determination of multiple frequencies in undersampled waveforms is studied using multiple smaller size discrete Fourier transforms (DFT). Given the sizes of multiple DFT, a range for the detectable frequencies in undersampled waveforms is presented for a set of general multiple frequencies. It is shown that, given multiple undersampling rates, the maximal range of the detectable multiple frequencies is the least common multiple of these multiple rates under the assumption that these rates are larger than twice of the maximal distance between the multiple frequencies.