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.

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.

Theory and algorithms for two-dimensional warped discrete Fourier transform

In this paper, the two-dimensional Warped Discrete Fourier Transform （2-D WDFT） is developed based on the concept of the 1-D WDFT. An exact computation algorithm is developed for 2-D WDFT based on matrix factorizing with special structure. A fast algorithm is then proposed to reduce greatly the computational complexity of the inverse 2-D WDFT. Finally, numerical examples are given to show the efficiency of the proposed approach.

Swept source optical coherence tomography based on non-uniform discrete fourier transform

A high-speed high-sensitivity swept source optical coherence tomography （SSOCT） system using a high speed swept laser source is developed. Non-uniform discrete fourier transform （NDFT） method is introduced in the SSOCT system for data processing. Frequency calibration method based on a Mach-Zender interferometer （MZI） and conventional data interpolation method is also adopted in the system for comparison. Optical coherence tomography （OCT） images from SSOCT based on the NDFT method, the MZI method, and the interpolation method are illustrated. The axial resolution of the SSOCT based on the NDFT method is comparable to that of the SSOCT system using MZI calibration method and conventional data interpolation method. The SSOCT system based on the NDFT method can achieve higher signal intensity than that of the system based on the MZI calibration method and conventional data interpolation method because of the better utilization of the power of source.

THE MULTIPLICATIVE COMPLEXITY AND ALGORITHM OF THE GENERALIZED DISCRETE FOURIER TRANSFORM(GFT)

In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.

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.

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.

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.

Peak-to-Average Power Ratio Performance Analysis for Orthogonal Chirp Division Multiplexing Multicarrier Systems Based on Discrete Fractional Cosine Transform

In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.

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.

Seismic dynamic stability of double-slider rock slopes containing tension cracks

Earthquakes have significant impact on rock slopes,thus studying the seismic stability of double-slider rock slopes containing tension cracks is crucial.We proposed an analysis method on the seismic dynamic slope stability.This method utilizes discrete Fourier transform to decompose real earthquake waves into a combination of harmonic waves.These waves are then used in conjunction with the pseudo-dynamic method and safety factor calculation formula to compute the safety factor.This approach accurately captures the influence of seismic time history characteristics on the dynamic stability of double-slider rock slopes containing tension cracks.The minimum safety factor in the obtained time history curves of the safety factor reflects the most unfavorable state of the slopes under seismic effects.Quantitative analysis is conducted using six sets of actual earthquake ground motion data obtained from the Pacific Earthquake Engineering Research Center’s NGAWest2 ground-shaking record database.The conclusions are as follows:(1)There is an inverse correlation between the average seismic acceleration amplitude and the minimum safety factor.Conversely,the seismic acceleration amplitude standard deviation shows a positive correlation with the minimum safety factor.The global sensitivity of geometric parameters in the slope model is higher than other influencing factors.(2)The proposed dynamic stability analysis method can capture the dynamic characteristics of earthquakes,emphasizing the minimum safety factor of the slope in the seismic time history as a stability indicator.In contrast,the pseudo-static method may yield unsafe results.(3)A safety factor expression considering hydrostatic pressure is proposed.A negative correlation was observed between the height of the water level line and the minimum safety factor.

Two modified discrete chirp Fourier transform schemes

This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes. Some matched filter properties such as the optimal selection of the transform length, and its relation-ship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theo-retical and simulation results have shown that the two MDCFTs can further improve the chirp rate reso-lution of the detected signals.

High-resolution algorithm based on temporal-spatial extrapolation

To enhance the resolution of parameter estimation with limited samples received by a short passive array, an iterative nonparametric algorithm for estimating the frequencies and direction-of-arrivals （DOAs） of signals is proposed. The cost function is constructed using 12-norm Gaussian entropy combined with an additional constraint, 12-norm constraint or linear constraint. By minimizing the cost functions in the temporal and the spatial dimensions using corresponding iteration algorithms respectively, the sparse discrete Fourier transforms （DFTs） of temporal and spatial samples are obtained to represent the extrapolated sequences with much larger sizes than the original samples. Then frequency and angle estimates are obtained by performing the traditional simple methods on the extrapolated sequences. It is shown that the proposed algorithm offers increased resolution and significantly reduced sidelobes compared with the periodogram and beamforming based methods. And it achieves high precision compared with the high-resolution method with lower computational burden. Some numerical simulations and real data processing results are presented to verify the effectiveness of the method.

A Feature-based Robust Digital Image Watermarking Against Desynchronization Attacks

In this paper, a new content-based image watermarking scheme is proposed. The Harris-Laplace detector is adopted to extract feature points, which can survive a variety of attacks. The local characteristic regions （LCRs） are adaptively constructed based on scale-space theory. Then, the LCRs are mapped to geometrically invariant space by using image normalization technique. Finally, several copies of the digital watermark are embedded into the nonoverlapped LCRs by quantizing the magnitude vectors of discrete Fourier transform （DFT） coefficients. By binding a watermark with LCR, resilience against desynchronization attacks can be readily obtained. Simulation results show that the proposed scheme is invisible and robust against various attacks which includes common signals processing and desynchronization attacks.

New shape clustering method based on contour DFT descriptor and modified SOFM neural network

A contour shape descriptor based on discrete Fourier transform （DFT） and a K-means al- gorithm modified self-organizing feature map （SOFM） neural network are established for shape clus- tering. The given shape is first sampled uniformly in the polar coordinate. Then the discrete series is transformed to frequency domain and constructed to a shape characteristics vector. Firstly, sample set is roughly clustered using SOFM neural network to reduce the scale of samples. K-means algo- rithm is then applied to improve the performance of SOFM neural network and process the accurate clustering. K-means algorithm also increases the controllability of the clustering. The K-means algo- rithm modified SOFM neural network is used to cluster the shape characteristics vectors which is previously constructed. With leaf shapes as an example, the simulation results show that this method is effective to cluster the contour shapes.

Windowing Techniques, the Welch Method for Improvement of Power Spectrum Estimation

This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch method.The discrete Fourier transform(DFT)is ubiquitous in digital signal processing(DSP)for the spectrum analysis and can be efciently realized by the fast Fourier transform(FFT).The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed.Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out.Therefore,windowing processing reduces the amplitude of the samples at the beginning and end of the window.In addition to selecting appropriate window functions,a pretreatment method,such as the Welch method,is effective to mitigate the spectral leakage.Due to the noise caused by imperfect,nite data,the noise reduction from Welch’s method is a desired treatment.The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio(SNR)is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction.The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected.The design of nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence of various window functions on the Fourier transform spectrum of the signals is discussed.Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.

The Impact of Agricultural Practices in China on Land-Atmosphere Interactions

Human-induced land use changes and the resulting alterations in vegetation features are major but poorly recognized drivers of regional climatic patterns.In order to investigate the impacts of anthropogenically-induced seasonal vegetation cover changes on regional climate in China,harmonic analysis is applied to 1982-2000 National Oceanic and Atmospheric Administration（NOAA） Advanced Very High Resolution Radiometer（AVVHRR）-derived normalized difference vegetation index（NDVI） time series（ten day interval data）.For two climatic divisions of South China,it is shown that the first harmonic term is in phase with air temperature,while the second and third harmonics are in phase with agricultural cultivation.The Penman-Monteith Equation and the Complementary Relationship Areal Evapotranspiration（CRAE） model suggest that monthly mean evapotranspiration is out of phase with temperature and precipitation in regions with signiffcant second or third harmonics.Finally,seasonal vegetation cover changes associated with agricultural cultivation are identiffed：for cropped areas,the temperature and precipitation time series have a single maximum value,while the monthly evapotranspiration time series has a bimodal distribution.It is hypothesized that multi-cropping causes the land surface albedo to sharply increase during harvesting,thereby altering the energy distribution ratio and contributing to observed seasonal vegetation cover changes.

Forecasting Daily Electric Load by Applying Artificial Neural Network with Fourier Transformation and Principal Component Analysis Technique

In this paper,we propose a hybrid forecasting model(HFM)for the short-term electric load forecasting using artificial neural network(ANN),discrete Fourier transformation(DFT)and principal component analysis(PCA)techniques in order to attain higher prediction accuracy.Firstly,we estimate Fourier coefficients by the DFT for predicting the next-day load curve with an ANN and obtain approximate load curves by applying the inverse discrete Fourier transformation.Approximate curves,together with other input variables,are given to the ANN to predict the next-day hourly load curves.Furthermore,we predict PCA scores to obtain approximate load curves in the first step,which are then given to the ANN again in the second step.Both DFT and PCA models use input variables such as calendrical and meteorological data as well as past electric loads.Applying those models for forecasting hourly electric load in the metropolitan area of Japan for January and May in 2018,we train our models using historical data since January 2008.The forecast results show that the HFM consisting of“ANN with DFT”and“ANN with PCA”predicts next-day hourly loads more accurately than the conventional three-layered ANN approach.Their corresponding mean average absolute errors show 2.7%for ANN with DFT,2.6%for ANN with PCA and 3.0%for the conventional ANN approach.We also find that in May,when electric demand is smaller with smaller fluctuations,forecasting errors are much smaller than January for all the models.Thus,we can conclude that the HFM would contribute to attaining significantly higher forecasting accuracy.

Automatic seizure detection with different time delays using SDFT and time-domain feature extraction

Automatic seizure detection is important for fast detection of the seizure because the way that the expert denotes and searches for seizure in the long signal takes time. The most common way to detect seizures automatically is to use an electroencephalogram(EEG). Many studies have used feature extraction that needs time for calculation. In this study, sliding discrete Fourier transform(SDFT) was applied for conversion to a frequency domain without using a window, which was compared with using window for feature selection. SDFT was calculated for each time series sample directly without any delay by using a simple infinite impulse response(IIR)structure. The EEG database of Bonn University was used to test the proposed method, and two cases were defined to examine a two-classifier feedforward neural network and an adaptive network-based fuzzy inference system. Results revealed that the maximum accuracies were 93% without delay and 99.8% with a one-second delay. This delay accrued because the average was taken for the results with a one-second window.

Research on Digital Watermark Using Pre-Processing Technology

We have realized a watermark embedding system based on audio perceptual masking and brought forward a watermark detection system using pre\|processing technology. We can detect watermark from watermarked audio without original audio by using this method. The results have indicated that this embedding and detecting method is robust, on the premise of not affecting the hearing quality, it can resist those attacks such as MPEG compressing, filtering and adding white noise.