A245320 Coefficients of "optimum L" polynomials L_n(ω^2) ordered by increasing powers.

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

Offset

0,9

Comments

Used in the generation of "optimum L" (or Legendre-Papoulis) filters.

References

A. Papoulis, ”On Monotonic Response Filters,” Proc. IRE, 47, No. 2, Feb. 1959, 332-333 (correspondence section)

Links

Table of n, a(n) for n=0..58.

C. Bond, Optimum “L” Filters: Polynomials, Poles and Circuit Elements, 2004.

C. Bond, Notes on “L” (Optimal) Filters, 2011.

A. Papoulis, Optimum Filters with Monotonic Response, Proc. IRE, 46, No. 3, March 1958, pp. 606-609.

Example

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

Crossrefs

Derived from A100258 and A060818.

Sequence in context: A109247 A021307 A170852 * A330341 A152893 A335682

Adjacent sequences: A245317 A245318 A245319 * A245321 A245322 A245323

Keyword

sign,tabl

Author

Jonathan Bright, Jul 17 2014

Status

approved