Unaliasing of undersampled spectra

Abstract

One of parts of digital signal processing is processing with undersampling. In this case, the sampling frequency is lower, than it is required by the sampling theorem. At undersampling, the spectrum of signals is distorted by an aliasing. Various ways of correction of the arising distortions are known. These ways are known under the name the unaliasing. In this article, one more method of the unaliasing is offered. It is offered to carry out multirate digital signal processing in parallel in two channels. Sampling frequencies in these channels are various. Both sampling frequencies are less, than the theorem of counting demands. The method is based on consecutive performance of several stages. At each stage on the next interval of frequencies, the part of a range is restored. Length of an interval is equal to a difference of two sampling frequencies. Therefore, the number of steps is defined by a relationship of width of the restored range and the interval size. For calculations, only subtraction operations are required. In paper, application of the offered way for restoration of a power range is shown. The same way can be applied also to complex Fourier-spectrum.