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Author Psarakis, Emmanouil Z. ♦ Moustakides, George V.
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Ideal Response ♦ An-based Method ♦ Transition Region ♦ Design Example ♦ Linear Equation ♦ Extensive Number ♦ Introduced Criterion ♦ Simple System ♦ Fourier Approximation ♦ Definite Superiority ♦ Suitable Quality Measure ♦ Remez Exchange Algorithm ♦ Significant Convergence Speed ♦ Index Term 1-d Digital Filter ♦ Design Requirement ♦ Actual Form ♦ Variational Technique ♦ Fourier Approximation Theory ♦ Various Class ♦ Optimum Solution ♦ Phase Fir Filter ♦ Complete Solution ♦ Unknown Part ♦ Proposed Measure ♦ Optimum Form ♦ Abstract Finite Impulse Response ♦ Non Min-max Design Technique ♦ Approximation Error Function ♦ Reduced Complexity ♦ Undefined Part ♦ Well-known Property ♦ Initialization Scheme ♦ Right Number ♦ Min Max Optimum Method
Abstract Abstract—Finite impulse response (FIR) filters obtained with the classical L 2 method have performance that is very sensitive to the form of the ideal response selected for the transition region. It is known that design requirements do not constraint in any way the ideal response inside this region. Most existing techniques utilize this flexibility. By selecting various classes of functions to describe the undefined part of the ideal response they develop methods that improve the performance of the L 2 based filters. In this paper we propose a means for selecting the unknown part of the ideal response optimally. Specifically by using a well-known property of the Fourier approximation theory we introduce a suitable quality measure. The proposed measure is a functional of the ideal response and depends on its actual form inside the transition region. Using variational techniques we succeed in minimizing the introduced criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. An extensive number of design examples show the definite superiority of our method over most existing non min-max design techniques, while the method compares very favorably with min–max optimum methods. Fi-nally we prove that the approximation error function of our filter has the right number of alternating extrema, required by the L 1 criterion, in the passband and stopband. This results in a significant convergence speed up, if our optimum solution is used as an initialization scheme, of the Remez exchange algorithm. Index Terms—1-D digital filters, Fourier approximation, zero phase FIR filters.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article