Use of the symmetrical number system in resolving single-frequency undersampling aliases

Abstract

The relationship between the discrete Fourier transform (DFT) and the symmetrical number system (SNS) is examined as a means of resolving single-frequency undersampling aliases (f>f/sub s//2). It is shown that the DFT naturally encodes the frequency information of a signal in a format that is in the same form as the SNS. Consequently, aliases that result from undersampling a signal can be resolved exactly using r/spl ges/2 channels. To demonstrate the concept, two- and three-channel examples are presented. Using the SNS properties of the DFT, the undersampling aliases can be easily resolved to a much greater extent than previously possible.