Discrete-time signal processing
Discrete-time signal processing
Ten lectures on wavelets
On the interpolation by discrete splines with equidistant nodes
Journal of Approximation Theory
SIAM Journal on Matrix Analysis and Applications
IEEE Transactions on Signal Processing
Frame-theoretic analysis of oversampled filter banks
IEEE Transactions on Signal Processing
Biorthogonal Butterworth wavelets derived from discreteinterpolatory splines
IEEE Transactions on Signal Processing
Interpolatory frames in signal space
IEEE Transactions on Signal Processing - Part I
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
Filter bank frame expansions with erasures
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
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We present a new family of frames, which are generated by perfect reconstruction filter banks. The filter banks are based on the discrete interpolatory splines and are related to Butterworth filters. Each filter bank comprises one interpolatory symmetric low-pass filter, one band-pass and one high-pass filters. In the sibling frames case, all the filters are linear phase and generate symmetric scaling functions with analysis and synthesis pairs of framelets. In the tight frame case, all the analysis waveforms coincide with their synthesis counterparts. In the sibling frame, we can vary the framelets making them different for synthesis and analysis cases. This enables us to swap vanishing moments between the synthesis and the analysis framelets or to add smoothness to the synthesis framelets. We construct dual pairs of frames, where all the waveforms are symmetric and the framelets may have any number of vanishing moments. Although most of the designed filters are IIR, they allow fast implementation via recursive procedures. The waveforms are well localized in time domain despite their infinite support.