By Topic

Waish-Hadamard Power Spectra Invariant to Certain Transform Groups

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)

Changes in Walsh-Hadamard power spectrum of an input pattern are investigated under several transformations: 1) shifting the elements of the input pattern cyclically, 2) enlarging and reducing the input pattern, 3) rotating the input pattern by multiples of 90°, and so on. Then the Walsh-Hadamard power spectrum is developed to be unchangeable by all the transformations through an introduced composing process. It may be considered as one of geometrical features. Every interesting geometrical property is generally invariant under some transformation groups. The composing process is available for obtaining functions having such group-invariant properties. The main idea is to make a linear combination of group-equivalent functions. First a G1-invariant power spectrum and next a permutation group on the G1-invariant power spectrum caused by G2 operating on the input pattern is found, thus arriving at a power spectrum being constant under both G1 and G2 through the composing process, where G1 and G2 are some transformation groups. Continuing this process, a power spectrum can be derived from the Walsh-Hadamard power spectrum that is invariant under a more general group of transformations.

Published in:

Systems, Man and Cybernetics, IEEE Transactions on  (Volume:9 ,  Issue: 4 )