# L(p)-approximation by the iteratively reweighted least squares method and the design of digital FIR filters in one dimension

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 Title: L(p)-approximation by the iteratively reweighted least squares method and the design of digital FIR filters in one dimension Barreto, Jose Antonio Burrus, Charles S. In this thesis a new and simple to program approach is proposed in order to obtain an $L\sb{p}$ approximation, 2 $<$ p $<$ $\infty$, based on the Iteratively Reweighted Least Squares (IRLS) method, for designing a linear phase digital finite impulse response (FIR) filter. This technique, interesting in its own right, can also be used as an intermediate design method between the least squared error and the minimum Chebyshev error criteria. Various IRLS algorithms are evaluated through comparison of the number of iterations required for convergence. It is shown that Kahng's (or Fletcher's et al) method with a modified acceleration technique developed in this work performs better, for most practical cases, than the other algorithms examined. A filter design method which allows different norms in different bands is proposed and implemented. An important extension of this method also considers the case of different p's (or different norms) in the stopband. Barreto, Jose Antonio. (1993) "L(p)-approximation by the iteratively reweighted least squares method and the design of digital FIR filters in one dimension." Masters Thesis, Rice University. http://hdl.handle.net/1911/13689. http://hdl.handle.net/1911/13689 1993