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- W1982527163 abstract "Some of the properties of optimal solutions to the finite-impulse-response low-pass filter design problem are discussed. These solutions are optimum in the sense of discrete Chebyshev approximation over a union of closed compact sets, i.e., the error of approximation exhibits at least <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(N + 3)/2</tex> alternations (of equal amplitude) over the frequency ranges of interest, where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>N</tex> is the duration of the filter impulse response in samples. It has been shown that, in certain special cases, the solution can exhibit <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(N + 5)/2</tex> alternations of equal amplitude. These solutions have been called extraripple filters because of the extra alternation that is present. How these extraripple solutions can, within bounds, be scaled to yield additional solutions, which are still optimal over new frequency ranges, is shown.' Thus an infinite number of optimal low-pass filters may be obtained directly from a finite number of extraripple solutions. An interpretation of the various types of optimal filters, in terms of locations of the zeros of the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>z</tex> - transform polynomial, is also given." @default.
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- W1982527163 date "1973-01-01" @default.
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- W1982527163 title "The predictability of certain optimum finite-impulse-response digital filters" @default.
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- W1982527163 doi "https://doi.org/10.1109/tct.1973.1083705" @default.
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