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A245320
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Coefficients of "optimum L" polynomials L_n(ω^2) ordered by increasing powers.
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0
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0, 0, 1, 0, 0, 1, 0, 1, -3, 3, 0, 0, 3, -8, 6, 0, 1, -8, 28, -40, 20, 0, 0, 6, -40, 105, -120, 50, 0, 1, -15, 105, -355, 615, -525, 175, 0, 0, 10, -120, 615, -1624, 2310, -1680, 490, 0, 1, -24, 276, -1624, 5376, -10416, 11704, -7056, 1764, 0, 0, 15, -280
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OFFSET
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0,9
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COMMENTS
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Used in the generation of "optimum L" (or Legendre-Papoulis) filters.
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REFERENCES
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A. Papoulis, ”On Monotonic Response Filters,” Proc. IRE, 47, No. 2, Feb. 1959, 332-333 (correspondence section)
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LINKS
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EXAMPLE
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Triangle begins:
0;
0, 1;
0, 0, 1;
0, 1, -3, 3;
0, 0, 3, -8, 6;
0, 1, -8, 28, -40, 20;
0, 0, 6, -40, 105, -120, 50;
...
So:
L_4(ω^2) = 0 + 0ω^2 + 3ω^4 - 8ω^6 + 6ω^8
L_5(ω^2) = 0 + 1ω^2 - 8ω^4 + 28ω^6 - 40ω^8 + 20ω^10
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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