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This study investigates the relationship between the moduli of continuity of a function and its Hartley transform. We explore this connection by deriving significant results such as the Riemann–Lebesgue lemma, Parseval's theorem, and the Hausdorff–Young inequality for the Hartley transform in both the Euclidean space and torus. Using a translation operator, we obtain an analog of Titchmarsh's theorem for the Hartley transform. In addition, we extend our analysis to the Hartley series on the torus. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this article is to study the solvability of Barbashin-type integro-differential equation and initial value problem via the structure of well-known generalized convolutions. We give necessary and sufficient conditions for the unique explicit solution of this class of equations and estimate its boundedness in certain weighted L1 spaces. The illustrative examples of the obtained results are also considered. [ABSTRACT FROM AUTHOR]

This paper is motivated by the ideas of fractional Fourier transform and Hartley transform. Looking towards the practicality and demanding attention of fractional Hartley transform we take keen interest into it. In this paper, we deal with inverse theorem of FRHT and some important properties of fractional Hartley transform like exponential rule, multiplication rule, transform of derivative and derivative of transform, which play a very crucial role in the development of fractional Hartley transform. [ABSTRACT FROM AUTHOR]

This research paper proposes a secure opto-audio cryptosystem using XORing mask and Hartley transform (HT). The digital one dimensional (1D) plainaudio data is converted into two dimensional plainaudio map (2D PAM) and after that, the 2D PAM is divided into 2D plainaudio blocks (2D PABs). The basic idea of the proposed opto-audio encryption system depends on XORing each block of the 2D PABs with a single image selected from a personal image database that can be viewed as a secret key in the proposed opto-audio cryptosystem. Each block of the mixed 2D PABs is then transposed using the chaotic logistic adjusted sine map (LASM) and optically encrypted with HT. The XOR and LASM are implemented digitally while HT implemented optically. An additional XORing mask step helps to remove residual intelligibility from the 2D PABs, fill in speechless gaps in spoken conversations, and destroy both the pitch and format details. The utilization of chaotic LASM allows efficient noise immunity. A comparative study is held between the proposed opto-audio encryption system and other related audio encryption systems in terms the standard well known encryption metrics. The results have confirmed the efficiency of the introduced opto-audio encryption system. The proposed opto-audio encryption system security is explored from an accurate encryption point of view, and tests confirmed the superiority of the proposed opto-audio encryption system from the encryption point of view.

The article describes the approach to the formation of a simulation model of information signals, which are typical for objects with different types of defects. The dispersive analysis of the signal spectrum components in the bases of the discrete Hartley transform and the discrete cosine transform is carried out. The analysis of the form of the reconstructed information signal is carried out depending on the number of coefficients of the spectral alignment in Hartley bases and cosine functions. The basis of orthogonal functions of a discrete argument is obtained, which can be used for the spectral transformation of information signals of a flaw detector. A method of simulation of information signals has been developed and experimentally investigated, which allows taking into account the deterministic and random components of the characteristics of real information signals. References 24, figures 13, tables 3. [ABSTRACT FROM AUTHOR]

Music instrument playing technique classification based on raw audio is a relatively unexplored area of music information retrieval research. This study systematically investigates the use of traditional audio features augmented by features based on the Hartley transform, used as input to a multiclass support vector machine (SVM) classifier, to identify up to 11 different playing techniques performed on each of the violin, viola, cello, and contrabass. Furthermore, 36- and 44-class joint instrument and playing technique classifiers were developed that achieved macro-average F-measures exceeding 0.88. Our approach expands and improves on the state-of-the-art study, which implemented sparse-coded magnitude and phase-derived spectral features. [ABSTRACT FROM AUTHOR]

Recently, most deep learning-based studies have focused on elaborately developing various types of neural networks in the spatial domain to tackle super-resolution. These methods usually have numerous parameters and require a huge amount of memory and time to train their networks. A frequency-domain neural network for super-resolution (FNNSR) has been presented. It designs a primitive neural network that can be trained using back propagation in the frequency domain. In this paper, we propose an improved FNNSR. In our method, the parameters of four quadrants in the compact weighting layer are shared. This substantially reduces the number of parameters in this layer. We use multiple convolutional layers with activations instead of a single convolution operator in FNNSR, so that the underlying features in transformed images can be learned. The Hartley transform is computed directly rather than through the Fourier transform. We design a new weighted Euclidean loss, which pays more attention to reconstructing the high-frequency part that is difficult to recover. Extensive experiments show that our method runs faster and requires fewer parameters than FNNSR. Though our method is not better than state-of-the-art methods in terms of quantitative performance, it still reveals encouraging results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Natural Sciences, Life & Applied Sciences is the property of Arab Journal of Sciences & Research Publishing (AJSRP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Four types of discrete transforms of Weyl orbit functions on finite point sets are developed. The point sets are formed by intersections of dual-root lattices with fundamental domains of affine Weyl groups. The finite sets of weights, labelling the orbit functions, obey symmetries of the dual extended affine Weyl groups. Fundamental domains of the dual extended affine Weyl groups are detailed in full generality. Identical cardinality of the point and weight sets is proved and explicit counting formulas for these cardinalities are derived. Discrete orthogonality of complex-valued Weyl and real-valued Hartley orbit functions over the point sets is established and the corresponding discrete Fourier–Weyl and Hartley–Weyl transforms are formulated. The unitary transform matrices of the discrete transforms are exemplified. [ABSTRACT FROM AUTHOR]

The article describes the approach to the formation of a simulation model of information signals, which are typical for objects with different types of defects. The dispersive analysis of the signal spectrum components in the bases of the discrete Hartley transform and the discrete cosine transform is carried out. The analysis of the form of the reconstructed information signal is carried out depending on the number of coefficients of the spectral alignment in Hartley bases and cosine functions. The basis of orthogonal functions of a discrete argument is obtained, which can be used for the spectral transformation of information signals of a flaw detector. A method of simulation of information signals has been developed and experimentally investigated, which allows taking into account the deterministic and random components of the characteristics of real information signals. References 24, figures 13, tables 3.

The Hartley transform, as in the case of the Fourier transform, is not suitably applicable to non-stationary representations of signals whose statistical properties change as a function of time. Hence, different versions of 2-D short time Hartley transforms (STHT) are given in comparison with the short time Fourier transform (STFT). Although the two different versions of STHT defined here with their inverses are equally applicable, one of them is mathematically incorrect/incompatible due to the incorrect definition of the 2-D Hartley transform in literature. These definitions of STHTs can easily be extended to multi-dimensions. Computations of the STFT and the two versions of STHTs are illustrated based on 32 channels (traces) of synthetic seismic data consisting of 256 samples in each trace. Salient features of STHTs are incorporated.

To ensure the confidentiality of color images during their storage or transmission on insecure networks, a number of encryption methods based on fractional transforms have been proposed and widely investigated. However, most of their outputs are complex values that are inconvenient for record and transmission. Also, those methods always deal with a whole color component with the same fractional-order and ignore the textural features that are contained in different image parts. In this paper, we first define a reality-preserving multiple-parameter fractional Hartley transform (RPMPFRHT), whose output is real value, and then a novel color image encryption method is proposed that divides the RGB components into different blocks and uses a constructed pixel scrambling operator to mix and hide the original color information. The outputs are transformed to different RPMPFRHT domains and further scrambled by a non-adjacent coupled map lattices system. Numerical simulations are performed to demonstrate that the proposed encryption algorithm is feasible, secure, sensitive to keys, and robust to potential attacks. [ABSTRACT FROM AUTHOR]

The modern real time applications such as orthogonal frequency division multiplexing, data/image/video compression, speech processing, and etc., demand high performance discrete orthogonal transform designs with lesser area/power and delay. This paper proposes two kinds of architectures to perform multiple N-point 1D-discrete orthogonal transforms on single chip. They are FFT parallel architecture based and matrix-vector multiplier based. The proposed architectures have the feasibility to perform N or N 2 or N 4 or N 8 -point discrete forward/reverse orthogonal transforms, where FFT, discrete Cosine, Sine, Haar, Hartley, Slant, and Walsh-Hadamard transforms are considered. The novelty with proposed architectures is the provision of multiple transforms using the single hardware. The frequency of the proposed 16-point FFT parallel architecture based and matrix-vector multiplier based 1D-discrete orthogonal transform architectures are 110.9 MHz and 26.65 MHz using 45 nm technology respectively. [ABSTRACT FROM AUTHOR]

In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed. [ABSTRACT FROM AUTHOR]

In this letter, layered discrete Hartley transform (DHT)-spread asymmetrically clipped optical-orthogonal frequency division multiplexing (LDHTS-ACO-OFDM) is presented; it uses DHT for multiplexing/demultiplexing and pulse-amplitude modulation (PAM) alphabets. LDHTS-ACO-OFDM yields several concrete enhancements over classical layered asymmetrically clipped O-OFDM (LACO-OFDM), such as low peak-to-average power ratio (PAPR), lower computational complexity, improved bit error rate (BER), and lower optical power penalty in a dispersive channel. Besides, LDHTS-ACO-OFDM augments the spectral efficiency relative to DHTS-ACO-OFDM with each addition of layer and ousts the inefficient bandwidth utilization limitation of DHTS-ACO-OFDM. [ABSTRACT FROM AUTHOR]

• An optical incoherent correlator was constructed using two digital micromirror devices (DMDs): the first DMD displays images of the recognized objects and the second DMD displays the hologram (holographic filter) generated using Hartley transform. • The objects have been successfully recognized in this correlator. • The reconstruction quality of Hartley transform-based holograms is not inferior to the Fourier transform ones. • Harley transform calculation uses less operations than Fourier transform and generated holograms have a smaller size. • The combined use of Hartley transform and DMD is preferred in high-speed encryption and recognition devices. High-speed optical reconstruction of holographic and diffractive optical elements is widely used in encryption and recognition, 3D-displays, beam shaping, nanofabrication, visualization, etc. This paper proposes the use of amplitude holograms generated by the Hartley transform (HT) as filters in an incoherent correlator. The real computations using the HT are faster and less computationally intensive than the standard complex transforms. Generated holograms using HT and Fourier transform (FT) were compared. It is demonstrated that the diffraction efficiency of HT-based holograms is not inferior to the FT case. The reconstruction quality is better in metrics (NSTD, MSE, SNR, RMS contrast, SSIM) by 2–10%. An optical incoherent correlator based on two digital micromirror devices (DMDs) was constructed. DMDs have very high frame rates (up to 30 kHz) that provides its great potential for application in fast recognition problems. The object images were displayed on the first DMD. The holograms generated with the HT were binarized and displayed on the second DMD. The objects were successfully recognized. Thus, HT-based amplitude holograms can be successfully used instead of FT-based amplitude holograms. [ABSTRACT FROM AUTHOR]

This paper presents a new method for evaluation and simulation of inrush current in various transformers using operational matrices and Hartley transform. Unlike most of the previous works, time and frequency domain calculations are conducted simultaneously. Mathematical equations are first represented to compute the inrush current based on reiteration and then Hartley transform is used to study harmonic effects in the frequency domain. Being a real valued function and accordingly giving results with the higher speed of calculations are the main features of Hartley transform. The inrush problem is initially solved for single-phase transformers for switching at different angles of the voltage waveform using this method and then the results of harmonic domain are compared with that of Fourier transform. The methodology is also applied to three-phase three-limb transformers since the analysis of their transient behavior is significant owing to the flux coupling interactions in multi-leg core structures. The feasibility and efficacy of the method is illustrated with appropriate circuits and MATLAB code is developed to get the time and frequency domain waveforms with high accuracy. The results are helpful to identify and evaluate inrush current harmonic effects in various transformers and hence the efficiency of the method is verified.

The choice of polling period sensors for measuring the speed and acceleration of the train can be produced using the spectral representation of functions of velocity and acceleration from time to time. Using the spectral method of determining the period of the survey, you can choose different value depending on the category of the train and its dynamic characteristics. For high-speed trains, the period of sensors is less than for trucks, since the latter are tightened by the transients during acceleration and deceleration. [ABSTRACT FROM AUTHOR]

The paper presents the results of a comparison study between the Fourier and the Hartley transforms for the real-time simulation of the sea surface elevation in 3D. Fourier transform s are currently the most used and efficient method for obtaining realistic ocean scenes in interactive Virtual Environments. Although the Fast Fourier Transform has been the preferred choice for this type of simulations, the study reveals that the Fast Hartley Transform can be a valid alternative, and even have some advantages compared to the former. The study mainly focuses on the performance and memory aspects, which are decisive factors for real-time applications with ocean scenes, such as ship bridge simulators. The methodology to obtain the sea surface elevation in time domain from a sea state defined by a directional wave spectrum is also described. [ABSTRACT FROM AUTHOR]

The relatively new Simpson Discrete Hartley Transform (SDHT) has interesting mathematical properties, which are crucial for applications. These are developed and proved in this paper. This analysis gives one a comprehensive understanding of the transform. [ABSTRACT FROM PUBLISHER]

We consider a new differential–difference operator Λ on the real line. We study the harmonic analysis associated with this operator. Next, we prove various mathematical aspects of the quantitative uncertainty principles, including Donoho–Stark’s uncertainty principle and variants of Heisenberg’s inequalities for its Hartley transform associated to the operator Λ . [ABSTRACT FROM AUTHOR]

We consider a new differential-difference operator $$\Lambda $$ on the real line. We study the harmonic analysis associated with this operator and we prove the Bochner and Bochner-Schwartz theorems, the Plancherel formula and the inversion theorems for the Hartley transform associated to the operator $$\Lambda $$ . [ABSTRACT FROM AUTHOR]

Sign language is an independent language that uses gestures and body language to convey meaning. Sign language recognition facilities the communication between deaf and community. In this paper, we investigated the use of different transformation techniques for extraction and description of features from an accumulation of signs’ frames into a single image. We show the performance of three transformation techniques (viz. Fourier, Hartley, and Log-Gabor transforms) applied on the whole and slices of the accumulated sign’s image. In addition, different classification schemes are tested and compared. Overall system’s accuracy reached over 99% for Hartley transform which is comparable with other works using the same dataset. [ABSTRACT FROM AUTHOR]

Boehmians are quotients of sequences which are constructed by using a set of axioms. In particular, one of these axioms states that the set S from which the denominator sequences are formed should be a commutative semigroup with respect to a binary operation. In this paper, we introduce a generalization of abstract Boehmian space, called generalized Boehmian space or G-Boehmian space, in which S is not necessarily a commutative semigroup. Next, we provide an example of a G-Boehmian space and we discuss an extension of the Hartley transform on it. [ABSTRACT FROM AUTHOR]

We consider a new differential-difference operatoron the real line. We study the harmonic analysis associated with this operator. Next, we prove various mathematical aspects of the quantitative uncertainty principles, including Donoho–Stark’s uncertainty principle and variants of Heisenberg’s inequalities for the Hartley transform associated to the operator. [ABSTRACT FROM PUBLISHER]

It is well known that the magnitude of transformer inrush current depends on several factors such as transformer construction and the angle of the applied voltage at the time of energization. In this paper, a novel approach is proposed to compute inrush current in both of time and frequency domains taking into consideration the significance of formulas derived based on magnetic circuit of five-limb transformer. Electric circuit nonlinear mathematical equations are applied to solve inrush problem based on iteration via MATLAB code. The comparison of the Harmonic domain simulation results obtained from Hartley transform with that of Fourier transform proves the capability of Hartley transform to accurately assess inrush current requiring less number of computations. [ABSTRACT FROM PUBLISHER]

The spectral analysis of the vertical effect of magnetic anomalies due to a 2-D horizontal circular cylinder is presented using Hartley transform. Hartley transform is an alternative approach to the famous complex Fourier transform. The depth to the center of the horizontal cylinder can be computed by a simple equation as a function of frequency. A synthetic example has been used to illustrate this technique and the validity of this approach has been proved by applying it to real data of a narrow band of quartz-magnetite in Mangampalli near Karimnagar town, India. The noise analyses were tested on the technique and showed a high level of confidence. The results of the field example are in good agreement with the ones published in the literature.