Open AccessLow‐complexity design framework of all‐pass filters with application in quadrature mirror filter banks design
Author(s) -
Jou YueDar,
Lin ZhanPei,
Chen FuKun
Publication year - 2017
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2016.0213
Subject(s) - toeplitz matrix , cholesky decomposition , mathematics , algorithm , hankel matrix , trigonometry , quadrature (astronomy) , filter (signal processing) , computational complexity theory , digital filter , quadrature mirror filter , computer science , low pass filter , prototype filter , mathematical analysis , electronic engineering , eigenvalues and eigenvectors , pure mathematics , physics , quantum mechanics , engineering , computer vision
Digital all‐pass filters design problem can be simplified by solving a set of linear equations associated with a Toeplitz‐plus‐Hankel matrix in the least‐squares sense. Consequently, the Cholesky decomposition or split Levinson technique can be appropriately used to obtain the optimal solution. In this study, the determination of the set of linear equations to calculate the all‐pass‐based quadrature mirror filter banks is achieved by exploiting some trigonometric identities and the frequency sampling method. The proposed simplification allows for expressing a sum of sinusoids by a single expression. The simulation results indicate that the presented new and simpler closed‐form expressions of the Toeplitz‐plus‐Hankel associated matrices can achieve accurate performance with a considerable reduction in computational complexity.