Least-squares design of two-dimensional recursive filters with specified magnitude and linear phase
type: Item
instance of: scholarly article
title: Least-squares design of two-dimensional recursive filters with specified magnitude and linear phase
zbMATH Open document ID: 0594.93060
DOI: 10.1016/0016-0032(86)90070-0
author: G. Shufelt
author: L. F. Chaparro
published in: Journal of the Franklin Institute
publication date: 1986-01-01T00:00:00Z
review text: A new method for the approximation of two-dimensional (2-D) digital recursive filters is presented. The approximating filter is a rational two-variable function whose coefficients \(a_ i\) and \(b_ i\) are to be found. The ideal filter is prescribed via \(\{g_ i(m,n)\}\), the set of ideal response values. To obtain a one-dimensional problem, the data are arranged according to the inverse lexicographic ordering. The canonical least-squares approximation leads to a set of nonlinear equations for the coefficients \(a_ i\) and \(b_ i\). Descent optimization methods based on iterative procedures can then be used. For the Gauss-Newton method, the Hessian of the error quadratic function must be calculated at each iteration. At the same time this method requires a good set of initial values. To this end a modified least-squares approximation previously derived by the author is used to obtain the initial value set. This last procedure is based on the theory of orthogonal polynomials on the unit disc. As examples of application, the design of the circular filter and that of the fan filter are presented. The results confirm the real advantages of the proposed design procedure.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93E25
Mathematics Subject Classification ID: 90C99
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 3956943
zbMATH Keywords: two-dimensional (2-D) digital recursive filters
zbMATH Keywords: least-squares approximation
zbMATH Keywords: Descent optimization
zbMATH Keywords: Gauss-Newton method
zbMATH Keywords: circular filter
zbMATH Keywords: fan filter
MaRDI profile type: Publication
full work available at URL: 0016-0032(86)90070-0
OpenAlex ID: W1990732926
cites work: Rational approximation of 2-D linear discrete systems
cites work: Q5652137
description: scientific article; zbMATH DE number 3956943