1,611 research outputs found
A fast algorithm for LR-2 factorization of Toeplitz matrices
In this paper a new order recursive algorithm for the efficient â1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, âŚ,p, of , as well as the elements of Râ1, of a Toeplitz matrix with dimensions L Ă p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix â1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and â1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed â1 algorithm is derived. Matlab code implementing the algorithm is also supplied
Two-Channel Speech Enhancement and Implementation Considerations: Noise Reduction and Speech Quality
Online learning of the transfer matrix of dynamic scattering media: wavefront shaping meets multidimensional time series
Thanks to the latest advancements in wavefront shaping, optical methods have
proven crucial to achieve imaging and control light in multiply scattering
media, like biological tissues. However, the stability times of living
biological specimens often prevent such methods from gaining insights into
relevant functioning mechanisms in cellular and organ systems. Here we present
a recursive and online optimization routine, borrowed from time series
analysis, to optimally track the transfer matrix of dynamic scattering media
over arbitrarily long timescales. While preserving the advantages of both
optimization-based routines and transfer-matrix measurements, it operates in a
memory-efficient manner. Because it can be readily implemented in existing
wavefront shaping setups, featuring amplitude and/or phase modulation and
phase-resolved or intensity-only acquisition, it paves the way for efficient
optical investigations of living biological specimens
On recursive least-squares filtering algorithms and implementations
In many real-time signal processing applications, fast and numerically stable algorithms for solving least-squares problems are necessary and important. In particular, under non-stationary conditions, these algorithms must be able to adapt themselves to reflect the changes in the system and take appropriate adjustments to achieve optimum performances. Among existing algorithms, the QR-decomposition (QRD)-based recursive least-squares (RLS) methods have been shown to be useful and effective for adaptive signal processing. In order to increase the speed of processing and achieve high throughput rate, many algorithms are being vectorized and/or pipelined to facilitate high degrees of parallelism. A time-recursive formulation of RLS filtering employing block QRD will be considered first. Several methods, including a new non-continuous windowing scheme based on selectively rejecting contaminated data, were investigated for adaptive processing. Based on systolic triarrays, many other forms of systolic arrays are shown to be capable of implementing different algorithms. Various updating and downdating systolic algorithms and architectures for RLS filtering are examined and compared in details, which include Householder reflector, Gram-Schmidt procedure, and Givens rotation. A unified approach encompassing existing square-root-free algorithms is also proposed. For the sinusoidal spectrum estimation problem, a judicious method of separating the noise from the signal is of great interest. Various truncated QR methods are proposed for this purpose and compared to the truncated SVD method. Computer simulations provided for detailed comparisons show the effectiveness of these methods. This thesis deals with fundamental issues of numerical stability, computational efficiency, adaptivity, and VLSI implementation for the RLS filtering problems. In all, various new and modified algorithms and architectures are proposed and analyzed; the significance of any of the new method depends crucially on specific application
Least Squares Problem for Adaptive Filtering
Abstract: We discus and demonstrate ways of deriving solutions to least squares problem in adaptive filtering without forming the conventional triangular system of equation, thus, generalized inverse techniques is used to obtain the tap weight coefficient vector when the autocorrelation matrix is singular, this approach is further extended using matrix inversion lemma to derive normal equation incorporating autocorrelation matrix and cross correlation vector
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