Аннотация:
This paper presents the type-II fast discrete Hartley transform (DHT-II) algorithms for
input data sequences of lengths from 2 to 8. The starting point for developing the eight algorithms is
the representation of DHT-II as a matrix–vector product. The underlying matrices usually have a
good block structure. These matrices must then be successfully factorized to obtain a computational
procedure that reduces the number of operations in computing the matrix–vector product. In some
cases, it is necessary to pre-decompose the original matrices into submatrices and rearrange the rows
and/or columns of the resulting matrices to find the factorizations that would substantially save
the arithmetic operations. As a result of applying the pointed transformations, we synthesized the
final algorithms with reduced computational complexity. The correctness of the obtained algorithmic
solutions was theoretically justified using the rigorous mathematical background of each of them.
Then, the complex algorithms were further tested using the MATLAB R2023b software to confirm their
performance. Finally, an evaluation of the computational complexity for each obtained solution was
compared with the computational complexity of the direct calculation of the matrix–vector product
and existing fast DHT-II algorithms. The obtained factorizations of the DHT-II transformation
matrices on average reduce the number of additions by 5% and the number of multiplications by 73%
compared with the direct calculation of the matrix–vector product.
