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.

Theory and algorithms for two-dimensional warped discrete Fourier transform

在这篇论文，二维的弄歪的分离 Fourier 变换(2-DWDFT ) 基于 1-D WDFT 的概念被开发。一个准确计算算法与特殊结构基于矩阵 factorizing 为 2-D WDFT 被开发。一个快算法然后被建议极大地减少反的 2-D WDFT 的计算复杂性。最后，数字例子被给显示出建议途径的效率。

Fractal Surface Synthesis Based on Two Dimensional Discrete Fourier Transform

The discrete Fourier transform(DFT)is used for fractional Brownian motion(FBM)surface synthesis in tribology(i.e.,contact,sliding,and sealing,etc).However,the relationship between fractal parameters(fractal dimension and scale factor)and traditional parameters,the influence of fractal parameters on surface appearance,have not been deeply discussed yet.These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic,required traditional parameters and geometric appearance.A quantitative relationship between fractal parameters and the root mean square deviation of surface(Sq)is derived based on the energy conservation property between the space and frequency domain of DFT.Under the stability assumption,the power spectrum of a FBM surface is composed of concentric circles strictly,a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension,scale factor,and sampling numbers,but the ten-point height(Sz),the skewness(Ssk)and the kurtosis(Sku)are still in random,where the probability distributions of Sz and Ssk are approximately normal distribution.Furthermore,by iterative searching,a surface with desired Abbott-Firestone curve could be obtained among those surfaces.An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components.Based on the relationship between Sq and surface energy,a filtering method of surface with controllable Sq is proposed.The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq,offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces,and makes it possible to control the Sq of surfaces after filtering.

Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.

A WEIGHTED GENERAL DISCRETE FOURIER TRANSFORM FOR THE FREQUENCY-DOMAIN BLIND SOURCE SEPARATION OF CONVOLUTIVE MIXTURES

This letter deals with the frequency domain Blind Source Separation of Convolutive Mixtures (CMBSS). From the frequency representation of the "overlap and save", a Weighted General Discrete Fourier Transform (WGDFT) is derived to replace the traditional Discrete Fourier Transform (DFT). The mixing matrix on each frequency bin could be estimated more precisely from WGDFT coefficients than from DFT coefficients, which improves separation performance. Simulation results verify the validity of WGDFT for frequency domain blind source separation of convolutive mixtures.

Authentication and Secret Message Transmission Technique Using Discrete Fourier Transformation

In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be transmitted over the network. Instead of direct embedding a message or image within the source image, choosing a window of size 2 x 2 of the source image in sliding window manner and then con-vert it from spatial domain to frequency domain using Discrete Fourier Transform (DFT). The bits of the authenticating message or image are then embedded at LSB within the real part of the transformed image. Inverse DFT is performed for the transformation from frequency domain to spatial domain as final step of encoding. Decoding is done through the reverse procedure. The experimental results have been discussed and compared with the existing steganography algorithm S-Tools. Histogram analysis and Chi-Square test of source image with embedded image shows the better results in comparison with the S-Tools.

Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.

Digital watermarking for still image based on discrete fractional fourier transform

Presents a digital watermarking technique based on discrete fractional Fourier transform (DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed technique is robust to lossy compression attack.

基于DFT的旋转变压器信号偏差矫正方法研究

解码芯片在对旋转变压器输出的位置信号做处理的过程中,芯片在采样时容易产生各种非理想偏差,这会造成转子位置估算精度的急剧下降。针对该问题,分析了电压信号中的幅值偏差和正交偏差会对旋转变压器解码的输出角度叠加一个2倍频的波动,直流偏差会叠加一个同频波动的问题,提出了一种基于离散傅里叶变换(DFT)的输入矫正法用于实现旋转变压器输出信号的偏差矫正,同时有效降低一次二次波动。该方法首先离散采样信号,通过DFT公式提取旋转变压器输出信号的直流信号和基频信号;然后基于直流信号和基频信号先后计算直流偏差、幅值偏差和正交偏差,通过控制器实现偏差值矫正。最后,仿真和试验结果表明,在芯片采样产生偏差时,所提出的偏差提取方法有效,试验中相应的正余弦输出信号指定阶次的波动更小。

Detecting Periodicity Associated with the Alpha-Helix Structure Using Fourier Transform

Alpha helix is a common type of secondary structure in the protein structure that consists of repeating helical turns. Patterns in the protein sequences that cause this repetitive pattern in the structure have long been sought. We used the discrete Fourier transform (DFT) to detect the periodicity signals correlated to the helical structure. We studied the distribution of multiple properties along the protein sequence, and found a property that showed strong periodicity correlated with the helical structure. Using a short-time Fourier transform (STFT) method, we investigated the amplitude of the periodical signals at each amino acid position. The results show that residues in the helix structure tend to display higher amplitudes than residues outside of the helices. This tendency is dramatically strengthen when sequence profiles obtained from multiple alignment were used to detect the periodicity. A simple method that predicted helices based on the amplitude yielded overall true positive rate (TPR) of 63%, 49% sensitivity, 72% specificity, and 0.22 Matthews Correlation Coefficient (MCC). The performance seemed to depend on the length of helices that the proteins had.

A Matrix Formulation of Discrete Chirp Fourier Transform Algorithms

This work presents a computational matrix framework in terms of tensor signal algebra for the formulation of discrete chirp Fourier transform algorithms.These algorithms are used in this work to estimate the point target functions(impulse response functions)of multiple-input multiple-output(MIMO)synthetic aperture radar(SAR)systems.This estimation technique is being studied as an alternative to the estimation of point target functions using the discrete cross-ambiguity function for certain types of environmental surveillance applications.The tensor signal algebra is presented as a mathematics environment composed of signal spaces,finite dimensional linear operators,and special matrices where algebraic methods are used to generate these signal transforms as computational estimators.Also,the tensor signal algebra contributes to analysis,design,and implementation of parallel algorithms.An instantiation of the framework was performed by using the MATLAB Parallel Computing Toolbox,where all the algorithms presented in this paper were implemented.

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.

分数阶Fourier变换的测不准原理

该文参考Fourier变换的性质研究了离散分数阶Fourier变换的测不准原理以及连续分数阶Fourier变换在Lebesgue测度下的测不准原理,使得分数阶Fourier变换的测不准原理性质更一般化.

Quantum Discrete Fourier Transform in an Ion Trap System

<正> We propose two schemes for the implementation of quantum discrete Fourier transform in the ion trap sys-tem.In each scheme we design a tunable two-qubit phase gate as the main ingredient.The experimental implementationof the schemes would be an important step toward complex quantum computation in the ion trap system.

Detection Algorithm for LFM Echo of Underwater Moving Targets Based on Discrete Fractional Fourier Transform

The mismatch between echo and replica caused by underwater moving target(UMT)'s radial velocity degrades the detection performance of the matched filter(MF)for the linear frequency modulation(LFM)signal.By using the focusing property of fractional Fourier transform(FRFT)to that signal,a detection algorithm for UMT's LFM echo based on the discrete fractional Fourier transform(DFRFT)is proposed.This algorithm is less affected by the target's radial velocity compared with the other MF detection algorithm utilizing zero radial velocity replica(ZRVR),and the mathematical relation between the output peak positions of these two algorithms exists in the case of existence of target echo.The algorithm can also estimate the target distance by using this relation.The simulation and experiment show that this algorithm'sdetection performance is better than or equivalent to that of the other MF algorithm utilizing ZRVR for the LFM echo of UMT with unknown radial velocity under reverberation noise background.

CONCURRENT SPEECHES SEPARATION USING WRAPPED DISCRETE FOURIER TRANSFORM

This letter proposes a new method for concurrent voiced speech separation. Firstly the Wrapped Discrete Fourier Transform (WDFT) is used to decompose the harmonic spectra of the mixed speeches. Then the individual speech is reconstructed by using the sinusoidal speech model. By taking advantage of the non-uniform frequency resolution of WDFT, harmonic spectra parameters can be estimated and separated accurately. Experimental results on mixed vowels separation show that the proposed method can recover the original speeches effectively.

基于滑窗DFT算法的新能源直流并网逆变器协调控制方法

当前的并网逆变器协调控制结构一般设置为独立形式,整体协调控制效率较低,导致周期逆变器的畸变率增加,为此提出基于滑窗离散傅里叶变换(Discrete Fourier Transform,DFT)算法的新能源直流并网逆变器协调控制方法。根据现有的测定需求和标准,先进行畸变电流测定,采用多目标的方式提高整体的协调控制效率。设计多目标交叉协调控制结构,构建滑窗DFT测算并网逆变器协调控制模型,采用三相平衡控制实现逆变器协调控制处理。测试结果表明,与传统带输出LC滤波器辅助逆变器协调控制方法和传统光伏处理逆变器协调控制方法相比,本次设计的基于滑窗DFT算法的逆变器协调控制方法最终得出的周期逆变器畸变率均被控制在0.2%以下,大幅提升了变网逆变器的协调控制效率,控制针对性增强,具有较好的实际应用价值。

Improved Speech Denoising Algorithm Based on Discrete Fractional Fourier Transform

The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform(DFRFT)is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio(SNR),and enhance the original speech signal.

Numerical Solution of Mean-Square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.