2014/09/16 by Binish Fatimah, Fatimah, Binish, Shashank Joshi +2
Computer Science · Mathematics · #Algorithm #Blind Source Separation Techniques #Computer science #Computer vision #Digital Filter Design and Implementation #FOS: Computer and information sciences #FOS: Mathematics #Filter (signal processing) #Filter bank #Image and Signal Denoising Methods #Information Theory (cs.IT) #Least-squares function approximation #Mathematics #SIGNAL (programming language) #Statistics #Statistics Theory (math.ST) #cs.IT #math.IT #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1409.5099
arxiv created 2014/09/16 · openalex publication_date 2014/09/16 · arxiv updated 2014/09/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In the companion paper, we proposed a concept of signal matched whitening filter bank and developed a time and order recursive, fast least squares algorithm for the same. Objective of part II of the paper is two fold: first is to define a concept of signal matched synthesis filter bank, hence combining definitions of part I and part II we obtain a filter bank matched to a given signal. We also develop a fast time and order recursive, least squares algorithm for obtaining the same. The synthesis filters, obtained here, reconstruct the given signal only and not every signal from the finite energy signal space (i.e. belonging to L2(R)), as is usually done. The recursions, so obtained, result in a lattice-like structure. Since the filter parameters are not directly available, we also present an order recursive algorithm for the computation of signal matched synthesis filter bank coefficients from the lattice parameters. The second objective is to explore the possibility of using synthesis side for modeling of a given stochastic process. Simulation results have also been presented to validate the theory.