Prime-factor algorithms for generalised discrete Hartley transform

A prime factor fast algorithm for the type-II generalised discrete Hartley transform is presented. In addition to reducing the number of arithmetic operations and achieving a regular computational structure, a simple index mapping method is proposed to minimise the overall implementation complexity     

New split-radix algorithm for the discrete Hartley transform

This paper presents a split-radix algorithm that can flexibly compute the discrete Hartley transforms of various sequence lengths. Comparisons with previously reported algorithms are made in terms of the required number of additions and multiplications. It shows that the length-3*2^m DHTs need a smaller number of multiplications than the length-2^m DHTs. However, they both require about the same computational complexity in terms of the total number of additions and multiplications. Optimized computation of length-12, -16 and -24 DFTs are also provided     

Split radix algorithm for the discrete Hartley transform

A new split radix fast algorithm for the discrete Hartley transform is presented. Comparisons with other reported algorithms are made in terms of the number of additions and multiplications. The algorithm is also simple and straightforward and can be easily implemented     

On prime factor mapping for the discrete Hartley transform

The authors propose a new prime factor mapping scheme, which requires no extra arithmetic operations for the realization of prime factor mapping, for the computation of the discrete Hartley transform (DHT). It is achieved by embedding all the extra arithmetic operations into the subsequent short-length computations, with the computational complexities of these embedded short lengths remaining unchanged. Consequently, the present approach significantly eliminates the burden which is introduced by the extra arithmetic operations. With this mapping scheme, it is further demonstrated that a prime-factor-mapped DHT would have superb performance compared with other fast DHT algorithms     

Computation of 2D discrete Hartley transform

Based on a decimation-in-time decomposition, a fast split-radix algorithm for the 2D discrete Hartley transform is presented. Compared to other reported algorithms, the proposed algorithm achieves substantial savings on the number of operations and provides a wider choice of transform sizes     

基于离散Hartley变换的OFDM实现模型

本文研究离散Hartley变换在OFDM系统中的应用,提出一种基于离散Hartley变换的OFDM实现模型.分析了新模型在加性高斯白噪声信道下的传输性能和算法复杂度.新模型与基于离散傅立叶变换(DFT)的OFDM系统具有相同的传输性能,但计算复杂度降低,时效性提高,且调制与解调算法一致.     

Fast computation of multidimensional discrete Hartley transform

Efficient algorithms for the fast computation of 2D and 3D discrete Hartley transforms have been proposed. It is shown that the proposed algorithms offer a significant saving in computation over the existing methods for various array sizes.<>     

Vector-radix algorithm for a 2-D discrete Hartley transform

A new multidimensional Hartley transform is defined and a vector-radix algorithm for fast computation of the transform is developed. The algorithm is shown to be faster (in terms of multiplication and addition count) compared to other related algorithms.     

Fast computation of discrete cosine transform through fast Hartley transform

A relationship between the discrete cosine transform (DCT) and the discrete Hartley transform (DHT) is derived. It leads to a new fast and numerically stable algorithm for the DCT.     

Fast algorithm for pseudodiscrete Wigner-Ville distribution usingmoving discrete Hartley transform

A new fast algorithm is proposed to compute pseudodiscrete Wigner-Ville distribution (PDWVD) in real-time applications. The proposed algorithm uses the moving discrete Hartley transform to compute the Hilbert transform and thereby implements the PDWVD in real domain. The computational complexity of the proposed algorithm is derived and compared with the existing algorithm to compute the PDWVD     

Fast radix-3/9 discrete Hartley transform

An efficient algorithm for computing radix-3/9 discrete Hartley transforms (DHTs) is presented. It is shown that the radix-3/9 fast Hartley transform (FHT) algorithm reduces the number of multiplications required by a radix-3 FHT algorithm for nearly 50%. For the computation of real-valued discrete Fourier transforms (DFTs) with sequence lengths that are powers of 3, it is shown that the radix-3/9 FHT algorithm reduces the number of multiplications by 16.2% over the fastest real-valued radix-3/9 fast Fourier transform (FFT) algorithm     

Scalable and modular memory-based systolic architectures for discrete Hartley transform

In this paper, we present a design framework for scalable memory-based implementation of the discrete Hartley transform (DHT) using simple and efficient systolic and systolic-like structures for short and prime transform lengths, as well as, for lengths 4 and 8. We have used the proposed short-length structures to construct highly modular architectures for higher transform lengths by a new prime-factor implementation approach. The structures proposed for the prime-factor DHT, interestingly, do not involve any transposition hardware/time. Besides, it is shown here that an N-point DHT can be computed efficiently from two (N/2)-point DHTs of its even- and odd-indexed input subsequences in a recursive manner using a ROM-based multiplication stage. Apart from flexibility of implementation, the proposed structures offer significantly lower area-time complexity compared with the existing structures. The proposed schemes of computation of the DHT can conveniently be scaled not only for higher transform lengths but also according to the hardware constraint or the throughput requirement of the application.     

Comments on "Generalized discrete Hartley transform"

The author comments on the paper by Hu et al. (IEEE Trans. Signal Processing, vol.40, no.12, p.2951-60, 1992). Information is provided about prior published work that precedes the transforms and convolution procedures defined in the above paper.<>     

Simple systolic arrays for discrete cosine transform

in this paper, simple 1-D and 2-D systolic array for realizing the discrete cosine transform (DCT) based on the discrete Fourier transform (DFT) fo an input sequence are presented. The proposed arrays are obtained by a simple modified DFT (MDFT) and an inverse DFT (IDFT) version of the Goertzel algorithm combined with Kung's approach. The 1-D array requiresN cells, one multiplier and takesN clock cycles to produce a completeN-point DCT. The 2-D array takes N clock cycles, faster than the 1-D array, but the area complexity is larger. A continuous flow of input data is allowed and no idle time is required between the input sequences.     

Fast computation of discrete Hartley transform via Walsh?Hadamard transform

A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh?Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.     

New fast algorithm to compute two-dimensional discrete Hartley transform

A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.<>     

Fast discrete cosine transform algorithm for systolic arrays

A fast algorithm for an N-point discrete cosine transform (DCT) is derived from a 4N-point Winograd Fourier transform algorithm (WFTA). This algorithm, which has the same form as Winograd's Fourier transform and convolution algorithms, is suitable for a high-speed implementation using one-bit systolic arrays.     

基于DHT的光OFDM系统PAPR抑制算法

针对光OFDM系统存在高峰均功率比(PAPR),提出了一种基于离散哈特利变换(DHT)的选择映射抑制算法。采用快速哈特利逆变换(IFHT)代替传统的快速傅立叶逆变换(IFFT)和Hermi t i an对称算法,并结合非对称限幅法产生满足光OFDM系统要求的正、实值信号送入光纤信道。     

Hartley series and notch Hartley transform

A new class of Hartley transform is introduced—the Hartley series (HS). The Hartley series is appropriate in the situation that the input signal is continuous and periodic in time, and hence its Hartley transform is discrete in frequency. Through this class of Hartley transform, any continuous and periodic signal can be decomposed into the weighted sum of cas functions (where cas (·) = cos (·) + sin (·)) In order to compute these Hartley coefficients, an algorithm referred to as the notch Hartley transform (NHT) is also presented. This algorithm can be applied to the input signal composed of arbitrary frequencies, and all Hartley coefficients can be computed in advance of the end of one period of the signal     

Vector Hartley transform

The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real. An algorithm for taking the Hartley transform of a long sequence on a multiprocessor machine by simultaneously transforming short subsequences does not require complex arithmetic and is faster than analogous techniques which use the Fourier transform.<>