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RESEARCH PRODUCT

Wavelet Frames Generated by Spline Based p-Filter Banks

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This chapter presents a design scheme to generate tight and so-called semi-tight frames in the space of discrete-time periodic signals. The frames originate from oversampled perfect reconstruction periodic filter banks. The filter banks are derived from discrete-time and discrete periodic splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pass filter, whose magnitude response mirrors that of a low-pass filter. In addition, these filter banks comprise a number of band-pass filters. In this chapter, frames generated by four-channel filter banks are briefly outlined (see Chap. 17 in [2] for details) and tight frames generated by six- and eight-channel filter banks are introduced. These latter frames provide an additional redundancy to the frame representations of signals. The design scheme enables us to design framelets with any number of local discrete vanishing moments (LDVMs). The computational complexity of the framelet transforms practically does not depend on the number of LDVMs and on the size of the impulse response of filters.