Accelerated graph-based spectral polynomial filters

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop on Machine Learning for Signal Processin

A new method for designing FIR filters with variable characteristics

This letter proposes a new method for designing finite-impulse response (FIR) filters with variable characteristics. The impulse response of the variable digital filter (VDF) is parameterized as a linear combination of functions in the spectral or tuning parameters. Using the least square objective function, the optimal solution is obtained by solving a system of linear equations. Design results show that this method is simple and effective in designing FIR VDF with good frequency characteristics. Furthermore, by using piecewise polynomial, instead of ordinary polynomial, more complicated frequency characteristics, or larger tuning range can be approximated.published_or_final_versio

A Lattice Basis Reduction Approach for the Design of Finite Wordlength FIR Filters

International audienceMany applications of finite impulse response (FIR) digital filters impose strict format constraints for the filter coefficients. Such requirements increase the complexity of determining optimal designs for the problem at hand. We introduce a fast and efficient method, based on the computation of good nodes for polynomial interpolation and Euclidean lattice basis reduction. Experiments show that it returns quasi-optimal finite wordlength FIR filters; compared to previous approaches it also scales remarkably well (length 125 filters are treated in < 9s). It also proves useful for accelerating the determination of optimal finite wordlength FIR filters