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Fixed-point filter and method

  • US 20040153484A1
  • Filed: 01/31/2003
  • Published: 08/05/2004
  • Est. Priority Date: 01/31/2003
  • Status: Abandoned Application
First Claim
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1. A method for fixed-point representation of a set of numbers, comprising:

  • (a) provide a set of numbers h(0), h(1), . . . , h(M) where M is a positive integer;

    (b) provide a first set of N integers, i1, i2, . . . , iN, . . . , iN, satisfying the following inequalities, 0<

    ii<

    i2<

    . . . <

    in<

    . . . <

    iN<

    M, where N is a positive integer smaller than M;

    (c) for each n in the range n=0, 1, . . . , N, and taking i0=0 and iN+1=M, find the smallest integer Bn such that −

    2Bn

    h(i)<

    2Bn for all h(i) in the nth bin defined as {h(in), h(in+1), . . . , h(in+1

    1)}, where Bn may be negative, zero, or positive;

    (d) for each h(i) in said nth bin, compute a corresponding quantized fixed-point coefficient ĥ

    (i) to precision based on said Bn from step (c);

    (e) for each h(i) compute the fixed-point quantization error Δ

    h(i)=h(i)−

    ĥ

    (i) where ĥ

    (i) is from step (d);

    (f) compute a total fixed-point quantization error from the results of step (e);

    (g) repeat steps (b)-(f) for at least a second set of N integers i1, i2, . . . , iN;

    (h) select a representation set of N integers from the sets of N integers of steps (b) and/or (g) where said representation set of N integers minimizes the total fixed-point quantization errors found in steps (e)-(g), and use said representation set of N integers to define the fixed-point representations of the numbers.

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