English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recent developments in quaternion-valued widely linear processing haveestablished that the exploitation of complete second-order statistics requiresconsideration of both the standard covariance and the three complementarycovariance matrices. Although such matrices have a tremendous amount ofstructure and their decomposition is a powerful tool in a variety ofapplications, the non-commutative nature of the quaternion product has beenprohibitive to the development of quaternion uncorrelating transforms. To thisend, we introduce novel techniques for a simultaneous decomposition of thecovariance and complementary covariance matrices in the quaternion domain,whereby the quaternion version of the Takagi factorisation is explored todiagonalise symmetric quaternion-valued matrices. This gives new insights intothe quaternion uncorrelating transform (QUT) and forms a basis for the proposedquaternion approximate uncorrelating transform (QAUT) which simultaneouslydiagonalises all four covariance matrices associated with improper quaternionsignals. The effectiveness of the proposed uncorrelating transforms isvalidated by simulations on both synthetic and real-world quaternion-valuedsignals.

Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing