Sliding Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform: Fast Algorithm and Applications

Abstract

This paper presents a fast algorithm for the computation of sliding conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT). The algorithm calculates the values of window <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> /4 from those of window <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> , one length- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> /4 Walsh Hadamard transform (WHT) and one length- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> /4 Modified WHT (MWHT). The proposed algorithm requires O( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) arithmetic operations, which is more efficient than the block-based algorithms of various transforms and the sliding FFT algorithm, but less efficient than the sliding WHT algorithms. Compared to the recently proposed sliding inverse SCHT (ISCHT) algorithm, the proposed algorithm is more efficient for real input but less efficient for complex input. The applications of the sliding CS-SCHT in transform domain adaptive filtering (TDAF) to complex signal channel equalization and real speech signal acoustic echo cancellation are also provided.