| Abstract: | The development of the wavelet theory has opened up many new applications in signal processing. In particular, wavelets are most appropriate for processing nonstationary signals when the time localization of events and the frequency localization are desired. After setting up the fundamentals of multiresolution analysis, we introduce the B-wavelets constructed by using the spline theory. Because of its non-orthogonal property on the same scale-levels, the dual wavelet is introduced so that a signal can be processed in real-time using the B-wavelets. A numerical algorithm is developed to decompose a signal into different resolutions (or frequency bands), so that each component may be processed individually. A reconstruction algorithm is used to recombine the processed components into the output signal. The window properties, the filter characteristics and the linear phase properties of the B-wavelet are discussed. Many examples showing various aspects of the B-wavelets are presented. |
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