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Generalized B-spline signal processing. (English) Zbl 0875.94086

Summary: This paper describes an efficient generalized B-spline filtering technique for the processing and representation of signals in terms of continuous generalized B-spline basis functions. Different types of generalized B-spline of any degree are introduced in a more generalized framework. An efficient generalized B-spline filtering technique for band-limited signal is presented. It is shown that the entire filtering process is equivalent to lowpass filtering of the band-limited signal. In the first stage of the filtering process, we consider the problem of extracting spline coefficients with down-sampling with a factor of m. In the second stage, we consider the reconstruction of the original signal through up-sampling with an optional zooming factor m. Normalized gain versus frequency response characteristics for some of the generalized B-spline filters are plotted for interpretation of the quality of generalized B-spline filtering. A computer simulation result is presented to show the antialiasing property of generalized B-spline filtering for band-limited signals.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E11 Filtering in stochastic control theory
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