The discrete Hartley transform (DHT) is becoming increasingly popular as a tool for the processing of real signals. Fast Hartley transform (FHT) algorithms exist which compute the DHT in a time proportional to N log2N. In many applications, such as interpolation and convolution of signals, a significant number of zeros is padded to the nonzero valued samples before the transform is computed. It is shown that for such situations, significant saving in the number of additions and multiplications can be obtained by pruning the FHT algorithm. The modifications in the FHT algorithm as a result of pruning are developed and implemented in an FHT subroutine. The amount of saving in the operation count is also determined. © 1991 IEEE.

Siva Bala Narayanan

K. M.Muraleedhara Prabhu

Computer Programming--Algorithms

ALGORITHM PRUNING

Discrete Hartley Transforms

Pruning

Mathematical transformations

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IIT Madras

Fast Hartley transform pruning

IEEE Transactions on Signal Processing

In this paper, we have applied the transform decomposition (TD) technique of pruning the fast Fourier transform (FFT) flow graph to the fast Hartley transform (FHT) flow graph. We have shown that efficient pruning is possible when the number of output points is limited. Any arbitrary band of spectra can also be computed using the method proposed. © 2005 Elsevier B.V. All rights reserved.

Microprocessors and Microsystems

Transform decomposition method of pruning the FHT algorithms

The least mean squared (LMS) algorithm and its variants have been the most often used algorithm in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infeasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS. © 2005 IEEE.

Fulltext

An analysis of real-fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

IEEE Transactions on Acoustics, Speech, and Signal Processing

Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data

IEEE Circuits and Devices Magazine

Domino-CMOS barrel switch for 32-bit VLSI processors

Electronics Letters

Comparative study of time efficiency of several algorithms for discrete W transform and discrete Hartley transform

IEEE Transactions on Computers

The Fast Hartley Transform Algorithm

Alternative to split-radix Hartley transform

Fast Hartley Transform Pruning

Journal	IEEE Transactions on Signal Processing
ISSN	1053587X
Open Access	No