New Decimation-In-Time Fast Hartley Transform Algorithm

IEEE Signal Processing Letters, 2000

IEEE Transactions on Circuits and Systems II: Express Briefs, 2000

In this correspondence, we propose a vector-radix algorithm for the fast computation of two-dimensional (2-D) discrete Hartley transform (DHT). For data sequences whose length is power of three, a radix-3×3 decimation in frequency algorithm is developed. It decomposes a length-N×N DHT into nine length-(N/3)×(N/3) DHTs. Comparison of the computational complexity with known algorithms shows that the proposed algorithm, in some cases, reduces significantly the number of arithmetic operations.

Circuits, Systems, and Signal Processing, 2017

This paper presents a new split-radix algorithm for DHT of length N = 2 n , called the Dual Split-Radix DHT (DSR DHT), that allows an efficient parallel implementation using a dual core system. Moreover, as it is different from existing split-radix algorithms for DHT, it offers an efficient hardware implementation similar to that for FFT. It avoids the so-called retrograde indexing specific to existing DHT algorithms that do not allow an efficient pipeline implementation.

Anais do I Congresso de Informática da Amazônia, 2001

A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast DHT algorithms and a multiplication-free fast algorithm for the Hadamard Transform.

IEEE Transactions on Signal Processing, 2001

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one-and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 2 2 algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms.

1993

Abstract Recently, a novel systolic structure has been proposed for the computation of DFT for transform length N= 4 M, M being prime to 4. This paper proposes a similar structure for the computation of DHT by prime factor decomposition. A new recursive algorithm is also proposed for computing DHT using a linear systolic array of cordic processing elements. The proposed structure has nearly the same hardware requirement as that of the corresponding DFT structure for real-valued data; but it yields significantly higher throughput

Journal of emerging technologies and innovative research, 2020

A discrete Hartley transform (DHT) algorithm can be efficiently implemented on a highly modular and parallel architecture having a regular structure is consisting of multiplier and adder. Discrete Hartley Transform (DHT) is one of the transform used for converting data in time domain into frequency domain using only real values. We have proposed a new algorithm for calculating DHT of length 2, where N=3 and 4. We have implemented Urdhwa multiplier based on compressor as an improvement in place of simple multiplication used in conventional DHT. This paper gives a comparison between conventional DHT algorithm and proposed DHT algorithm in terms of delays and area. Keywords— Discrete Hartley Transform (DHT), Urdhwa Multiplier, 4:2 Compressor, 7:2 compressor and Xilinx Vertex family.

IET Signal Processing, 2014

A general method for efficient computation of four types of discrete Hartley transform using cyclic convolutions is considered. Forming hashing arrays on the basis of simplified arguments of basis transform for synthesis of efficient algorithm is analysed. The hashing arrays in the algorithm define partitioning of the harmonic basis into Hankel submatrices. The examples of four types of discrete Hartley transforms using the proposed method are presented.

IEEE/SBrT International Telecommunication Symposium, ITS 2010, 2010

A new fast algorithm for computing the discrete Hartley transform (DHT) is presented, which is based on the expansion of the transform matrix. The algorithm presents a better performance, in terms of multiplicative complexity, than previously known fast Hartley transform algorithms. A detailed description of the computation of DHTs with blocklengths 8 and 12 is shown. The algorithm is very attractive for blocklengths N ≥ 128.

2000 10th European Signal Processing Conference, 2000

The three-dimensional discrete Hartley transform (3-D DHT) has been proposed as an alternative tool to the 3-D discrete Fourier transform (3-D DFT) for 3-D applications when the data is real. The 3-D DHT has been applied in many three-dimensional image and multidimensional signal processing applications. This paper presents a fast three-dimensional algorithm for computing the 3-D DHT. The mathematical development of this algorithm is introduced and the arithmetic complexity is analysed and compared to related algorithms. Based on a single butterfly implementation, this algorithm is found to offer substantial savings in the total number of multiplications and additions over the familiar row-column approach.