The Duality of Leakage and Aliasing and Improved Digital Spectral Analysis Techniques

Abstract

When processing, recording, and analyzing continuous, analog signals or functions with a digital computer, information is lost when the signals are converted to digital form. When signals are sampled in one domain (time or frequency), the loss of information is characterized as aliasing in the other (frequency or time, respectively) domain. When a signal or function is truncated in one domain, the information loss is characterized as leakage in the other domain. It is shown that because of the dual nature of leakage and aliasing, that leakage in one domain reduces aliasing in the other domain and visa-versa. Examples of reducing leakage or aliasing in each domain by the dual in the other domain are given to illustrate. Since current art has not used time aliasing to reduce frequency leakage previously, a time alias processor for this purpose is described. A flat-top window function with spectral one frequency line in width is used in conjunction with the time alias processor to maintain leakage to within the nearest frequency line.