DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

This paper is concerned with the Diophantine properties of the sequence {ξθ~n},where 1≤ξ<θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μ_λ with λ = θ^(-1) as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak,who consider the case of Bernoulli convolutions. As an application,we prove that μ_λ almost every x is normal to any base b ≥ 2,which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

ABOUT THE FOURIER TRANSFORMS OF NON-SMOOTH MEASURES ON HYPERSPHERES

If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.

FAST FOURIER TRANSFORMS ON BINARY FIELDS

We give a unified treatment of Fast Fourier Transforms for UDMD systems which contains , as special cases, Fast Fourier algorithms for character groups of many subgroups associated with binary fields.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations

We study solutions to convolution equations for functions with discrete support in R^n, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in C^n, and we determine possible domains in terms of the properties of the convolution operator.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Dual Image Cryptosystem Using Henon Map and Discrete Fourier Transform

This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.

GP Algorithm-Based Fourier Transform Infrared Spectrum Trend Term Removal Model

Trend term removal is a key step in Fourier transform infrared spectroscopy(FTIR)data pre-processing.The most commonly used least squares(LS)method,although satisfying the real-time requirement,has many problems such as highly correlated initial values of the expression parameters,the need to pre-estimate the trend term shape,and poor fitting accuracy at low signal-to-noise ratios.In order to achieve real-time and robust trend term removal,a new trend term removal method using genetic programming(GP)in symbolic regression is constructed in this paper,and the FTIR simulation interference results and experimental measurement data for common volatile organic compounds(VOCs)gases are analyzed.The results show that the genetic programming algorithm can both reduce the initial value requirement and greatly improve the trend term accuracy by 20%-30% in three evaluation indicators,which is suitable for gas FTIR detection in complex scenarios.

High-sensitive state perception method for inverter-fed machine turn insulation based on FrFT-Mel

Amidst the swift advancement of new power systems and electric vehicles,inverter-fed machines have progressively materialized as a pivotal apparatus for efficient energy conversion.Stator winding turn insulation failure is the root cause of inverter-fed machine breakdown.The online monitoring of turn insulation health can detect potential safety risks promptly,but faces the challenge of weak characteristics of turn insulation degradation.This study proposes an innovative method to evaluate the turn insulation state of inverter-fed machines by utilizing the fractional Fourier transform with a Mel filter(FrFT-Mel).First,the sensitivity of the high-frequency(HF)switching oscillation current to variations in turn insulation was analyzed within the fractional domain.Subsequently,an improved Mel filter is introduced,and its structure and parameters are specifically designed based on the features intrinsic to the common-mode impedance resonance point of the electrical machine.Finally,an evaluation index was proposed for the turn insulation state of inverter-fed machines.Experimental results on a 3kW permanent magnet synchronous machine(PMSM)demonstrate that the proposed FrFT-Mel method significantly enhances the sensitivity of turn insulation state perception by approximately five times,compared to the traditional Fourier transform method.

Assessment of portable FTIR and Raman spectroscopy for the detection of 2,3-dimethyl-2,3-dinitrobutane(DMDNB)in plastic explosives

The Marplex Convention was established to prevent the manufacture of unmarked plastic explosives and stipulates that a volatile detection agent must be added at the time of manufacture.However,to-date,laboratory testing remains the internationally accepted practice for identifying and quantifying the taggants stipulated in the Convention.In this project,portable FTIR and Raman instruments were tested for their ability to detect 2,3-dimethyl-2,3-dinitrobutane(DMDNB),the chemical marker incorporated in plastic explosives that are manufactured within Australia.While both FTIR and Raman instruments detected solid DMDNB(98%purity),field analysis of plastic explosives at an Australian Defence establishment showed that both FTIR and Raman spectra were matched the relevant explosive(RDX or PETN),rather than the DMDNB taggant.For all three plastic explosives tested,the concentration of DMDNB was measured by SPME-GC-MS to be between 1.8 and 2%,greater than the minimum 1%concentration stipulated by the Marplex Convention.Additional testing with a plastic explosive analogue confirmed that the minor absorption peaks that would characterize low concentrations of DMDNB were masked by absorption bands from other compounds within the solid.Thus,while both FTIR and Raman spectroscopy are suitable for detection of plastic explosives,neither rely on the presence of DMDNB for detection.It is likely that similar results would be found for other taggants stipulated by the Marplex Convention,given they are also present in concentrations less than 1%.

Security-Enhanced Directional Modulation Based on Two-Dimensional M-WFRFT

Directional modulation(DM)is one of the most promising secure communication techniques.However,when the eavesdropper is co-located with the legitimate receiver,the conventional DM has the disadvantages of weak anti-scanning capability,anti-deciphering capability,and low secrecy rate.In response to these problems,we propose a twodimensional multi-term weighted fractional Fourier transform aided DM scheme,in which the legitimate receiver and the transmitter use different transform terms and transform orders to encrypt and decrypt the confidential information.In order to further lower the probability of being deciphered by an eavesdropper,we use the subblock partition method to convert the one-dimensional modulated signal vector into a twodimensional signal matrix,increasing the confusion of the useful information.Numerical results demonstrate that the proposed DM scheme not only provides stronger anti-deciphering and anti-scanning capabilities but also improves the secrecy rate performance of the system.

Localization method of subsynchronous oscillation source based on high-resolution time-frequency distribution image and CNN

The penetration of new energy sources such as wind power is increasing,which consequently increases the occurrence rate of subsynchronous oscillation events.However,existing subsynchronous oscillation source-identification methods primarily analyze fixed-mode oscillations and rarely consider time-varying features,such as frequency drift,caused by the random volatility of wind farms when oscillations occur.This paper proposes a subsynchronous oscillation sourcelocalization method that involves an enhanced short-time Fourier transform and a convolutional neural network(CNN).First,an enhanced STFT is performed to secure high-resolution time-frequency distribution(TFD)images from the measured data of the generation unit ports.Next,these TFD images are amalgamated to form a subsynchronous oscillation feature map that serves as input to the CNN to train the localization model.Ultimately,the trained CNN model realizes the online localization of subsynchronous oscillation sources.The effectiveness and accuracy of the proposed method are validated via multimachine system models simulating forced and natural oscillation events using the Power Systems Computer Aided Design platform.Test results show that the proposed method can localize subsynchronous oscillation sources online while considering unpredictable fluctuations in wind farms,thus providing a foundation for oscillation suppression in practical engineering scenarios.

Aerial target threat assessment based on gated recurrent unit and self-attention mechanism

Aerial threat assessment is a crucial link in modern air combat, whose result counts a great deal for commanders to make decisions. With the consideration that the existing threat assessment methods have difficulties in dealing with high dimensional time series target data, a threat assessment method based on self-attention mechanism and gated recurrent unit(SAGRU) is proposed. Firstly, a threat feature system including air combat situations and capability features is established. Moreover, a data augmentation process based on fractional Fourier transform(FRFT) is applied to extract more valuable information from time series situation features. Furthermore, aiming to capture key characteristics of battlefield evolution, a bidirectional GRU and SA mechanisms are designed for enhanced features.Subsequently, after the concatenation of the processed air combat situation and capability features, the target threat level will be predicted by fully connected neural layers and the softmax classifier. Finally, in order to validate this model, an air combat dataset generated by a combat simulation system is introduced for model training and testing. The comparison experiments show the proposed model has structural rationality and can perform threat assessment faster and more accurately than the other existing models based on deep learning.

Enhanced Steganalysis for Color Images Using Curvelet Features and Support Vector Machine

Algorithms for steganography are methods of hiding data transfers in media files.Several machine learning architectures have been presented recently to improve stego image identification performance by using spatial information,and these methods have made it feasible to handle a wide range of problems associated with image analysis.Images with little information or low payload are used by information embedding methods,but the goal of all contemporary research is to employ high-payload images for classification.To address the need for both low-and high-payload images,this work provides a machine-learning approach to steganography image classification that uses Curvelet transformation to efficiently extract characteristics from both type of images.Support Vector Machine(SVM),a commonplace classification technique,has been employed to determine whether the image is a stego or cover.The Wavelet Obtained Weights(WOW),Spatial Universal Wavelet Relative Distortion(S-UNIWARD),Highly Undetectable Steganography(HUGO),and Minimizing the Power of Optimal Detector(MiPOD)steganography techniques are used in a variety of experimental scenarios to evaluate the performance of the proposedmethod.Using WOW at several payloads,the proposed approach proves its classification accuracy of 98.60%.It exhibits its superiority over SOTA methods.

An Efficient Radar Detection Method of Maneuvering Small Targets

Detection of maneuvering small targets has always been an important yet challenging task for radar signal processing.One primary reason is that target variable motions within coherent processing interval generate energy migrations across multiple resolution bins,which severely deteriorate the parameter estimation performance.A coarse-to-fine strategy for the detection of maneuvering small targets is proposed.Integration of small points segmented coherently is performed first,and then an optimal inter-segment integration is utilized to derive the coarse estimation of the chirp rate.Sparse fractional Fourier transform(FrFT)is then employed to refine the coarse estimation at a significantly reduced computational complexity.Simulation results verify the proposed scheme that achieves an efficient and reliable maneuvering target detection with-16dB input signal-to-noise ratio(SNR),while requires no exact a priori knowledge on the motion parameters.

Design of a Multifrequency Signal Parameter Estimation Method for the Distribution Network Based on HIpST

The application of traditional synchronous measurement methods is limited by frequent fluctuations of electrical signals and complex frequency components in distribution networks.Therefore,it is critical to find solutions to the issues of multifrequency parameter estimation and synchronous measurement estimation accuracy in the complex environment of distribution networks.By utilizing the multifrequency sensing capabilities of discrete Fourier transform signals and Taylor series for dynamic signal processing,a multifrequency signal estimation approach based on HT-IpDFT-STWLS(HIpST)for distribution networks is provided.First,by introducing the Hilbert transform(HT),the influence of noise on the estimation algorithm is reduced.Second,signal frequency components are obtained on the basis of the calculated signal envelope spectrum,and the interpolated discrete Fourier transform(IpDFT)frequency coarse estimation results are used as the initial values of symmetric Taylor weighted least squares(STWLS)to achieve high-precision parameter estimation under the dynamic changes of the signal,and the method increases the number of discrete Fourier.Third,the accuracy of this proposed method is verified by simulation analysis.Data show that this proposed method can accurately achieve the parameter estimation of multifrequency signals in distribution networks.This approach provides a solution for the application of phasor measurement units in distribution networks.

Quantifying Kinematic Tremor in an NGLY1-Deficient Individual: A Case Study

NGLY1 Deficiency is an autosomal recessive congenital disorder that has been identified in less than 100 individuals. Most individuals with NGLY1 Deficiency display hyperkinetic movement disorders, including choreiform, athetoid, dystonic myoclonic, dyskinetic, and dysmetric movements. Developing a consistent and concise consensus on the classification and evaluation of tremors is essential to forward the research and treatment of tremors. It has also been reported that some individuals with NGLY1 Deficiency demonstrate tremor, but such tremor has never been formally investigated. The primary objective of this study is to determine if an individual with NGLY1 Deficiency demonstrates an identifiable tremor during a series of arm movements and, if so, describe the frequency and power characteristics of that tremor. Arm movement kinematics were obtained using a 16-camera Vicon system, and time series trajectory waveforms for three planes of a marker placed on the hand were developed. Custom MATLAB scripts were utilized to compute Fast Fourier Transformations of the data within the identified waveform segments. A mean frequency of 2.30 Hz (SD = 1.05) with a mean power of 5.02 |P1(f)| (SD = 4.63) suggests that our participant’s kinematic data did display a persistent tremor in both hands across all tasks and movement planes. Analyses of the reaching hand and the non-reaching hand suggest the participant displayed an action tremor in both postural and intention (kinetic) tremors. Future directions should include assessing additional individuals with NGLY1 Deficiency to determine if the tremor is a distinguishable disorder behavior. Additionally, evaluating other anatomical sites, such as the elbow, head, and lower limbs, would provide further insights into the characteristics of this tremor.

Enhanced Wideband Frequency Estimation via FFT: Leveraging Polynomial Interpolation and Array Indexing

Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.