Kafri, Wasfi S.; Hashlamoun, Wael \(N\)-dimensional phase approximation in the \(L_\infty\)-norm. (English) Zbl 0990.93071 Multidimensional Syst. Signal Process. 11, No. 3, 257-275 (2000). A commonly used technique to approximate a prescribed phase in a frequency region consists of, according to a desired phase response, seeking the coefficients of an \(N\)-dimensional digital all-pass filter such that the maximum design error is minimized in the frequency region.Extending a work of the first author concerning the one-dimensional case [W. S. Kafri, Signal Process. 57, No. 2, 163-175 (1997)] and making use of the theory of nonlinear Chebyshev approximation, multidimensional phase function properties are investigated. The characterization of the best approximation as a global minimum is emphasized. The approximation on discrete point sets in a compact multidimensional domain is also considered and several illustrative examples included. Reviewer: Pablo Gonzalez-Vera (La Laguna) Cited in 1 Document MSC: 93C62 Digital control/observation systems 41A50 Best approximation, Chebyshev systems Keywords:phase approximations; digital all-pass filter; nonlinear Chebyshev approximation; best approximation PDFBibTeX XMLCite \textit{W. S. Kafri} and \textit{W. Hashlamoun}, Multidimensional Syst. Signal Process. 11, No. 3, 257--275 (2000; Zbl 0990.93071) Full Text: DOI