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 lineshape one frequency line in width is used in conjunction with the time alias processor to maintain leakage to within the nearest frequency line.
[1]
Ronald N. Bracewell,et al.
The Fourier Transform and Its Applications
,
1966
.
[2]
Michael Athans,et al.
A Frequency-Domain Estimator for Use in Adaptive Control Systems
,
1987,
1987 American Control Conference.
[3]
A. Papoulis.
Signal Analysis
,
1977
.
[4]
W. Press,et al.
Numerical Recipes: The Art of Scientific Computing
,
1987
.
[5]
P. V. D. Hof,et al.
Quantification of model uncertainty from data: input design, interpolation, and connection with robust control design specifications
,
1992,
1992 American Control Conference.
[6]
William H. Press,et al.
Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition
,
1987
.