Fast Algorithms for the Computation of Sliding Sequency-Ordered Complex Hadamard Transform

Abstract

Fast algorithms for computing the forward and inverse sequency-ordered complex Hadamard transforms (SCHT) in a sliding window are presented. The first algorithm consists of decomposing a length-N inverse SCHT (ISCHT) into two length-N/2 ISCHTs. The second algorithm, calculating the values of window i+N/4 from those of window i and one length-N/4 ISCHT and one length-N/4 modified ISCHT (MISCHT), is implemented by two schemes to achieve a good compromise between the computation complexity and the implementation complexity. The forward SCHT algorithm can be obtained by transposing the signal flow graph of the ISCHT. The proposed algorithms require O(N) arithmetic operations and thus are more efficient than the block-based algorithms as well as those based on the sliding FFT or the sliding DFT. The application of the sliding ISCHT in transform domain adaptive filtering (TDAF) is also discussed with supporting simulation results.

An efficient algorithm for the conjugate symmetric sequency-ordered complex Hadamard transform

“…This property makes the CS-SCHT distinguishable from all the other existing complex Hadamard transforms reported in [12]- [21]. Furthermore, due to the conjugate-symmetric property of the CS-SCHT, only one-half of the spectrum is needed to be computed for the analysis and synthesis of real-valued signals, which leads in memory and computation savings.…”

Discrete Fractional COSHAD Transform and Its Application

“…Thus, the computation of the transform of a signal consists of additions and subtractions of the signal samples. The Hadamard transform and many of its variations, such as the sequency-ordered complex Hadamard transform (SCHT) [4,5] and the Jacket transform [6], have been proposed, and their applications to image processing and communications have been reported [7].…”