

A240908


The sequency numbers of the 8 rows of a version of the HadamardWalsh matrix of order 8.


4




OFFSET

1,2


COMMENTS

The Hadamard (HadamardWalsh) matrix is widely used in telecommunications and signal analysis. It has 3 wellknown forms which vary according to the sequency ordering of its rows: "natural" ordering, "dyadic" or Payley ordering, and sequency ordering. In a mathematical context the sequency is the number of zero crossings or transitions in a matrix row (although in a physical signal context, it is half the number of zero crossings per time period). The matrix row sequencies are a permutation of the set [0,1,2,...n1], where n is the order of the matrix. For spectral analysis of signals the sequencyordered form is needed. Unlike the dyadic ordering (given by A153141), the natural ordering requires a separate list for each matrix order. This sequence is the natural sequency ordering for an order 8 matrix.


LINKS

Table of n, a(n) for n=1..8.
N. J. A. Sloane, A Library of Hadamard Matrices
Eric Weisstein's World of Mathematics, Hadamard Matrix
Wikipedia, Walsh matrix


FORMULA

Recursion: H(2)=[1 1; 1 1]; H(n) = H(n1)*H(2), where * is Kronecker matrix product.


EXAMPLE

This is a fixed length sequence of only 8 values, as given.


CROSSREFS

Cf. A240909 "natural order" sequencies for HadamardWalsh matrix, order 16.
Cf. A240910 "natural order" sequencies for HadamardWalsh matrix, order 32.
Cf. A153141 "dyadic order" sequencies for HadamardWalsh matrix, all orders.
Cf. A000975(n) is sequency of last row of H(n).  William P. Orrick, Jun 28 2015
Sequence in context: A097517 A127559 A066747 * A117043 A013664 A154173
Adjacent sequences: A240905 A240906 A240907 * A240909 A240910 A240911


KEYWORD

nonn,fini,full


AUTHOR

Ross Drewe, Apr 14 2014


EXTENSIONS

Definition of H(n) corrected by William P. Orrick, Jun 28 2015


STATUS

approved



