Study about Novel Recursive Algorithm for Realization of One-Dimensional Discrete Hartley Transform | Chapter 09 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 In digital signal processing, the discrete Hartley transform is a useful tool. This work introduces a new recursive approach for realising the one-dimensional discrete Hartley transform of even length. The Chebyshev Polynomial is used to construct the transform after folding the input data once. A single folding technique can process twice as much data as previous methods. The proposed algorithm reduces the amount of adds and multiplications when compared to previous techniques. The recursive algorithms are suitable for implementation in VLSI. Multiplications take longer than additions to complete. Because the number of multiplications in the suggested method is significantly lower than in certain other structures, the proposed algorithm can save time in its implementation.

Author(S) Details

M. N. Murty
Department of Physics, National Institute of Science & Technology, Berhampur - 761008, Odisha, India.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6555

Study on Matrix Inverse as by-Product of Determinant | Chapter 10 | Theory and Practice of Mathematics and Computer Science Vol. 7

The determinant of a given square matrix is obtained by iterative matrix order condensation as a product of pivot elements evaluated. As a by-product, it follows that the inverse of this matrix is then evaluated through the extension of the iterative matrix order. Only simple elementary arithmetical operations without any high mathematical process are involved in the fast and straightforward basic iterative method. Remarkably, without failing the inverse of any square matrix, the revised optimal iterative method would compute within minutes, whether real or complex, singular or non-singular, and interestingly enough even for size as big as 999x999. If the calculation of small size inverse matrices is feasible, the manually extended iteration procedure is often generated to shorten the iteration steps.

Author (s) Details

Feng Cheng Chang
Allwave Corporation, Torrance, California, USA.

View Book :- https://stm.bookpi.org/TPMCS-V7/issue/view/18