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.

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.

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.

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.

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.

Support-Limited Generalized Uncertainty Relations on Fractional Fourier Transform

This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bounds are related to FRFT parameters and signal lengths, were derived in theory. These uncertainty principles disclose that the data in FRFT domains may have?much higher concentration than that in traditional time-frequency domains, which will enrich the ensemble of generalized uncertainty principles.

Discrete Entropic Uncertainty Relations Associated with FRFT

Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.

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.

Research progress on discretization of fractional Fourier transform

As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform （including 3 main types： linear combination-type; sampling-type; and eigen decomposition-type）, and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.

相位差测量的FFT法和DTFT法误差分析

对噪声背景下FFT法和DTFT法的相位差测量误差进行了分析。应用误差理论,分别推导出了高斯白噪声背景下FFT法和DTFT法的相位差估计均方根误差的计算公式。针对不同的泄漏误差系数、采样序列长度和信噪比条件,进行了计算机仿真验证,仿真结果与公式计算结果相吻合。理论分析和仿真结果均表明,对于相同的信噪比和采样序列长度,DTFT法的相位差估计均方根误差在理论上为一恒定值,且始终等于FFT法估计误差的理论下限。

基于FFT的一种计及负频率影响的相位差测量新方法

用FFT法测量低频正弦信号相位差时,精度明显下降,甚至无法测量,其主要原因之一是模型中忽略了负频率成分的贡献。基于FFT法,提出了一种计及负频率影响的相位差测量方法,分别给出了加矩形窗和加汉宁窗对应的相位差计算公式。仿真结果表明,在无噪声背景下,具有很高的精度,尤其是加汉宁窗后,误差接近双精度运算的下限;在噪声背景下,该方法的测量精度也高于FFT法。提出的测量方案简单实用,特别适用于频率很低或接近奈奎斯特频率的正弦信号相位差测量。

DFT与FFT在实际应用时的性能比较

分析了离散傅立叶变换 (DFT)和它的快速算法 (FFT)的计算 ,对DFT和FFT在应用时的特点作了深入的比较 。

插值FFT和滑动DTFT的科氏流量计信号处理方法

科氏流量计通过计算一次仪表输出的两路同频正弦信号的时间差来测量质量流量。实时精确估计两路信号的频率和相位差是科氏流量计数字信号处理的关键。针对科氏流量计实测信号,提出一种基于插值FFT和滑动DTFT的信号处理方法。利用插值FFT估计信号频率,通过计及负频率的改进滑动DTFT估计相位差,进而计算出时间差。方法兼顾了参数的估计精度和算法的计算效率,对比实验表明了该方法的有效性和优越性。

离散分数阶Fourier变换的LFM信号时延估计

根据Ozaktas的采样型离散分数阶Fourier变换算法,针对线性调频信号,结合分数阶Fourier变换对线性调频(LFM)信号的独特聚集性,研究了基于Ozaktas离散分数阶Fourier变换的含多普勒的LFM信号时延估计,给出了线性调频体制雷达分数阶Fourier域的目标检测与测距具体实现,并与经典数字脉压对雷达目标测距的分辨力、时延估计误差、运算量进行对比分析,结果验证了基于Ozaktas离散分数阶Fourier变换时延估计的可行性及有效性。

一种NDVI时间序列离散Fourier重建方法

时间序列重建是多时相遥感变化监测研究的基础。多时相遥感数据由于气象、轨道周期等原因,很难达到严格意义的同时相。不同时相的特征信息不具有可比性。以一矿区归一化差值植被指数为例,采用2004-2007年SPOT II/IV数据,通过大气校正,波段运算,获得7个时相的包括伪不变特征区和矿业扰动区8个实验工作面的NDVI最大值、均值和振幅;进而采用快速Fourier变换的Fourier 4模型将NDVI转化为振幅,将物候信息转化为相位。实现了低数据样本下高时间、高空间分辨率NDVI时间序列数据集重建。该方法可为多时相遥感信息时间序列归一化、多源数据时间序列同化以及特征信息协同反演提供一些借鉴。

离散分数阶Fourier变换的阶数分解算法

分数阶Fourier变换在科学计算和工程中有广泛应用前景,但现有的离散分数阶Fourier变换(DFRFT)缺乏有效的快速算法。本文给出了一种采用阶数分解的DFRFT算法,由特定阶数DFRFT的加权和可得到任意分数阶域的DFRFT,权系数由DFTHermite本征值和附加零构成序列的离散Fourier反变换(IDFT)得到,且在搜索最佳分数阶域的过程中仅需计算一次IDFT,无需重新计算其所有变换核,从而可有效减少运算量,适合于应用在分数阶域的多分量信号检测和滤波处理中,仿真结果表明了该算法的有效性。

二维离散分数阶Fourier变换的双混沌图像加密算法

针对现今分数阶Fourier变换和传统混沌加密的不足,提出了一种基于二维离散分数阶Fourier变换的双混沌图像加密算法。该算法首先借助明文图像信息生成辅助密钥矩阵与输入密钥相结合得到混沌序列,再将生成的中间密文作为二维离散分数阶Fourier变换输入,最后进行置乱操作,使得明文信息得到很好的隐藏。通过实验仿真表明,该算法不仅能有效抵抗统计特征攻击、差分攻击,而且大大改善经传统分数阶Fourier变换后直方图像不平滑的缺点,达到很好的加密效果。

基于全相位FFT的稳健型时间调制阵列测向

基于谐波特征分析的时间调制阵列测向方法的正确性与精度严重依赖接收谐波的估计精度.传统的离散傅里叶变换(discrete Fourier transform,DFT)或快速傅里叶变换(fast Fourier transform,FFT)在估计谐波的幅相时,由于信号频率通常偏离采样频率的整数倍,会形成栅栏效应,从而引起基于谐波特征分析的时间调制阵列测向的精度降低甚至失效.针对该问题,本文将全相位FFT引入二单元时间调制阵列接收谐波的分析中,通过提升谐波幅相估计的鲁棒性来提升时间调制阵列测向方法的稳健性.仿真结果表明,当信号的载频为频谱分辨率的任意小数倍时,提出的全相位FFT时间调制阵列测向方法均能正确测向,且随着信噪比的增加,测向均方根误差收敛至0.本文工作提升了基于谐波特征分析的单通道时间调制阵列测向方法的稳定性.

基于离散分数阶Fourier变换本征矢量分解的图像加密算法

针对目前采用分数阶傅里叶变换对图像进行加密的算法中,其主要存在密钥敏感性较差等不足,提出一种将离散分数阶Fourier变换与指数随机相位掩膜、Logistic混沌映射结合起来进行加密的新算法。该算法在加密过程采用离散分数阶Fourier变换本征矢量分解的方法进行运算,显著提高了加密系统的安全性能。首先,对原始图像进行Logistic映射混沌置乱处理,接着与第一个指数随机矩阵A相乘,之后再经α阶离散的分数阶Fourier变换;其次,与第二个指数随机矩阵B相乘,再经β阶离散的分数阶Fourier变换;最后,利用Logistic映射对图像再次进行置乱处理来获得最终的密文图像。仿真结果表明:与其他类似加密机制相比,该加密系统兼顾了更强的密钥敏感性以及更高的安全性。