The fast Hartley transform (FHT) and fast W transform (FWT) algorithm for,solving welLconditioned r-circulant equations is presented in this paper. The arithmetic operation save about half compared with the fast Fouri...The fast Hartley transform (FHT) and fast W transform (FWT) algorithm for,solving welLconditioned r-circulant equations is presented in this paper. The arithmetic operation save about half compared with the fast Fourier transform (FFT) algorithm. For ill-condotioned cases, an efficient numerical stable methods for solving r-circulant equations is suggested by using FHT, FWT and truncated singualr value decomposition (TSVD) method. An open problem is solved.展开更多
In this paper, the Multi-dimensional Polynomial Transform is used to convert the Multi-dimensional W Transform (MDDWT) into a series of one-dimensional W transform (DWT). Thus, a new polynomial transform algorithms fo...In this paper, the Multi-dimensional Polynomial Transform is used to convert the Multi-dimensional W Transform (MDDWT) into a series of one-dimensional W transform (DWT). Thus, a new polynomial transform algorithms for MDDWT is obtained. The algorithm needs no complex number operations and is simple in structure. The number of multiplications for computing a r-d DWT is only times that of the common used row-column method. The number of additions is also reduced considerablely. Running time of the algorithm on micro-computers is given and is compared with the common used row-column method.展开更多
文摘The fast Hartley transform (FHT) and fast W transform (FWT) algorithm for,solving welLconditioned r-circulant equations is presented in this paper. The arithmetic operation save about half compared with the fast Fourier transform (FFT) algorithm. For ill-condotioned cases, an efficient numerical stable methods for solving r-circulant equations is suggested by using FHT, FWT and truncated singualr value decomposition (TSVD) method. An open problem is solved.
文摘In this paper, the Multi-dimensional Polynomial Transform is used to convert the Multi-dimensional W Transform (MDDWT) into a series of one-dimensional W transform (DWT). Thus, a new polynomial transform algorithms for MDDWT is obtained. The algorithm needs no complex number operations and is simple in structure. The number of multiplications for computing a r-d DWT is only times that of the common used row-column method. The number of additions is also reduced considerablely. Running time of the algorithm on micro-computers is given and is compared with the common used row-column method.
