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.

FAST IMPLEMENTATION OF CONVOLUTION BACKPROJECTION ALGORITHM IN SPOTLIGHT SAR

A fast implementation of the convolution backprojection（CBP）algorithm in spotlight synthetic aperture radar（SAR）is presented based on the fast Fourier transform（FFT）.Traditionally,the computation of the ＇backprojection＇ process is expensive,since resampling in the process is implemented by using the interpolation operation.By analyzing the relative location relationship among different pixels,the algorithm realizes the ＇backprojection＇ using a series of FFTs instead of the interpolation operation.The point target simulation validates that the new algorithm accelerates the CBP algorithm,and the computational rate increases about 85%.

Walsh Hadamard Transform Based Transceiver Design for SC-FDMA with Discrete Wavelet Transform

This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access(OFDMA)with extra advantage of low Peak to Average Power Ratio(PAPR). Moreover,this article also suggests the application of Walsh Hadamard transform(WHT)for linear precoding(LP)to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform(FFT)based SCFDMA is shown through simulated results in terms of PAPR,spectral efficiency(SE)and bit error rate(BER).

Experiments in Parallelizing the Type IV Discrete Cosine Transform

The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method for computing Fourier transforms, the authors present parallel implementations of two new algorithms developed for the type IV Discrete Cosine Transform （DCT-IV） which support the new interleaved fast Fourier transform method. The authors discuss the realizations of their implementations using two paradigms. The first involved commodity equipment and the Message-Passing Interface （MPI） library. The second utilized the RapidMind development platform and the Cell Broadband Engine （BE） processor. These experiments indicate that the authors＇ rotation-based algorithm is preferable to their lifting-based algorithm on the platforms tested, with increased efficiency demonstrated by their MPI implementation for large data sets. Finally, the authors outline future work by discussing an architecture-oriented method for computing DCT-IVs which promises further optimization. The results indicate a promising fresh direction in the search for efficient ways to compute Fourier transforms.

Scheme for Designing the 1-D Convolution Window of Gabor Filter

A scheme for designing one-dimensional (1-D) convolution window of the circularly symmetric Gabor filter which is directly obtained from frequency domain is proposed. This scheme avoids the problem of choosing the sampling frequency in the spatial domain, or the sampling frequency must be determined when the window data is obtained by means of sampling the Gabor function, the impulse response of the Gabor filter. In this scheme, the discrete Fourier transform of the Gabor function is obtained by discretizing its Fourier transform. The window data can be derived by minimizing the sums of the squares of the complex magnitudes of difference between its discrete Fourier transform and the Gabor function's discrete Fourier transform. Not only the full description of this scheme but also its application to fabric defect detection are given in this paper. Experimental results show that the 1-D convolution windows can be used to significantly reduce computational cost and greatly ensure the quality of the Gabor filters. So this scheme can be used in some real-time processing systems.

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.

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。

半导体激光自混合变速测量的离散Chirp-Fourier变换方法

当外部激光被反射回激光内腔时,反馈光与激光器腔内光混合,调制激光器的输出功率和频率,通过信号处理可以得到物体运动的多普勒频率,从而计算出物体的运动速度。基于这种特性,设计出一种激光自混合干涉仪,为了知道该技术是否适用于变速测量,对激光自混合用于变速运动物体的速度测量进行了探索。基于激光自混合三镜腔模型,建立了激光自混合用于变速测量的数学模型,提出了基于该模型的特征参量提取方法,该方法基于离散Chirp-Fourier变换理论。对激光自混合输出信号进行离散Chirp-Fourier变换,变换结果的主瓣坐标反映了物体运动的速度及加速度信息。最后,对该方法进行了仿真分析,在SNR=0 dB和SNR=7 dB的情况下,能较好地获得物体的速度和加速度信息。因此,仿真试验证明:该方法在较低信噪比的情况下仍能有效提取物体的速度及加速度信息。

离散Fourier变换并行算法综述

本文详细介绍了 1 - D DFT精确计算的六步框架并行算法和按位并行计算法 ,以及按位计算法在 2 - D Mesh和 Torus上的模拟实现 ,同时介绍了近似计算中的基于奇异值分解的算法和基于快速多极方法的算法。对于 2 - D DFT,本文介绍了并行行列算法和并行多项式变换算法 ,并分析了其优缺点。

二维离散余弦变换与二维离散Fourier变换的快速算法

文中提出N×M2D—DCT(Ⅱ)的一种快速算法,其需实运算量为:M_u=1/2NMlog_2N+1/4MNlog_2M,A_d=3/2NMlog_2NM—3MN—1/2M^2+M+N(其中N、M为2的幂)。当N=M时,与文[5]的结果一样、这是目前最好的结果。但文[5]算法不稳定,容易产生较大的误差。本文克服了这一缺点。并利用此2D—FCT(Ⅱ)导出了2D—DCT.2D—DST和2D—DCST的快速算法及2D—DFT的一种快速算法。2D—DFT快速算法的运算量与文[1]中用FPT计算2D—DFT相近。

基于Fourier变换离散化的连续小波变换频域算法

对于固定的尺度,小波变换是待分析信号与小波基函数的线性卷积。当小波基函数的Fourier变换有显式表达式时,利用其Fourier变换进行线性卷积称为小波变换的频域计算方法。由于线性卷积的长度大于信号的长度,因此,选取线性卷积中的哪一部分作为小波变换的系数也是一个亟需回答的问题。本文利用Fourier变换的离散化和离散Fourier变换的关系由小波变换时域算法推导了小波变换频域算法,证明了时域算法与频域算法的等价性;解释了这两种方法分别应该选取线性卷积中的哪一部分作为小波变换的系数;分析了频域算法产生边界效应的原因;给出了频域算法中参数的选取方法,以便克服边界效应。时间复杂度分析以及数值实验均表明了频域算法至少比时域算法减少了1/3的运行时间。

长度不同的二维离散Fourier变换的向量编码算法

离散傅里叶变换(Discrete Fourier Transform,DFT)在信号处理上扮演着非常重要的角色。本文给出了各维长度不同的二维DFT快速算法。这种算法利用了对于高维整点的向量编码(vectorcoding)技术。与传统的行列算法相比较大大减少了乘法数量和迭代次数,并且省去了对数据的转置。这种方法可以推广到更高维的DFT上。本文以二维为例,向量编码算法(简称VC算法)与行列算法相比,在加法次数相同的情况下,乘法次数约为行列算法的四分之三,迭代次数更是减少了一半。

基于Faster-RCNN及一维曲线分析的表计指针识读方法

针对机器人部署调试中表计需逐个配置的问题,提出基于神经网络学习及一维曲线分析的表盘指针、刻度识别方法。基于Faster-RCNN(faster region-based convolutional network),初步识别刻度盘位置,从而确定指针运动圆心。将图像以圆心为中心进行极坐标展开后,通过分析一维曲线的频域特征筛选刻度所在区域,统计不同区域灰度峰谷值的形式确定刻度和指针的真实位置。最后对几种典型表计进行实验分析,验证所提方法的有效性。实验结果显示,该方法对表计样本量较多的表计类型,可成功实现自动读数功能。

基于多注意力机制的纹理感知视频修复方法

针对现有视频修复方法无法有效利用远处空间内容信息而导致修复结果中存在结构和纹理不合理的问题,提出了一种基于多注意力机制的纹理感知视频修复方法。该方法设计了由多头时空注意力和单图局部注意力构成的多注意力机制以保证全局结构并增强局部纹理,其中多头时空注意力关注整体时空信息,单图局部注意力通过局部窗口的自注意力机制精炼提取局部信息。另外,采用可即插即用的快速傅里叶卷积层残差块代替前馈网络中的普通卷积,将感受野扩展为整个图像,进一步增强了模型对图像纹理和结构的全局信息的获取能力。快速傅里叶卷积层残差块和单图局部注意力相辅相成,共同提升局部纹理的修复质量。在YouTube-VOS和DAVIS数据集上的实验结果表明,虽然提出的方法修复结果的客观质量评价仅次于最优方法Fuseformer,但其参数量和运行时间分别下降了54.8%和21.5%,而且能够生成视觉上更逼真、语义上更合理的修复内容。

基于DFT与ECA的滚动轴承故障诊断

针对滚动轴承故障诊断中传统卷积神经网络(convolutional neural networks,简称CNN)提取特征的感受野受限于卷积核大小的问题,提出了一种结合离散傅里叶变换(discrete Fourier transform,简称DFT)和高效通道注意力(efficient channel attention,简称ECA)的卷积神经网络模型(convolutional neural network combining discrete Fourier transform and efficient channel attention,简称DFT-ECANet)。首先,将原始振动信号通过DFT变换到频域,在频域上经卷积和离散傅里叶逆变换(inverse discrete Fourier transform,简称IDFT)转换到时域,使信号在时域上具有全局的感受野;其次,将该信号与经过卷积的数据在通道维度上进行拼接,通过ECA为各通道数据分配权重,并关注诊断性能高的特征;最后,通过多个卷积-池化层进一步提取模型深层特征,结合池化层和全连接层诊断轴承故障。实验结果表明:DFT-ECANet在原始振动数据集上具有较高的诊断精度和较好的泛化性能,通过T分布随机近邻嵌入(T-distributed stochastic neighbor embedding,简称T-SNE)可降维可视化模型的诊断过程;在强噪声干扰下仍能保持较高的精度,具备较强的鲁棒性和抗噪性能。

一种基于CNN与FFT‑ELM的输电线路故障识别与定位方法

及时、准确地检测输电线路故障类型与位置是提高电力系统可靠性最重要的问题之一,为此提出一种基于卷积神经网络(convolutional neural networks,CNN)与基于快速傅里叶变换(fast Fourier transform,FFT)的极限学习机(extreme learning machine,ELM)分类模型并行的输电线路故障识别及定位方法。首先,以故障电压时序图作为输入,构建CNN;然后,利用FFT将时域故障电压数据分解,提取各频段的电压峰值与相角作为故障特征样本;接着,以提取的故障特征样本集作为输入,构建ELM网络;最后,通过特征融合层将2个神经网络进行融合,输出故障类型和定位结果。实验结果表明,此方法对输电线路故障识别的准确率为99.95%、故障定位误差在500 m以内、平均误差为263.5 m,可靠性优于其他模型。

基于混合卷积窗六谱线插值的多普勒信号处理

激光多普勒测速系统信号处理的过程中,通常采用快速傅里叶变换提取多普勒频移进而计算出被测物体运动速度,由于频谱泄露和栏栅效应的影响,会导致测量精度降低。本文提出了一种四项Nuttall窗和五项Rife-Vincent窗的混合卷积窗函数结合改进的六谱线插值算法来降低频谱泄露和栏栅效应所带来的影响,从而提高激光多普勒信号处理精度。搭建了双光束后向散射差动式激光多普勒测速平台,通过仿真和实测得出在加入了R_(SN)=-10 dB的高斯白噪声的情况下使用该混合卷积窗所测量的最小相对误差为0.0027%,而分别使用两个单一的窗函数测量的最小相对误差分别为0.0103%和0.0461%。从而验证了本方法的有效性。

Fast Fourier transform convolutional neural network accelerator based on overlap addition

In convolutional neural networks(CNNs), the floating-point computation in the traditional convolutional layer is enormous, and the execution speed of the network is limited by intensive computing, which makes it challenging to meet the real-time response requirements of complex applications. This work is based on the principle that the time domain convolution result equals the frequency domain point multiplication result to reduce the amount of floating-point calculations for convolution. The input feature map and the convolution kernel are converted to the frequency domain by the fast Fourier transform(FFT), and the corresponding point multiplication is performed. Then the frequency domain result is converted back to the time domain, and the output result of the convolution is obtained. In the shared CNN, the input feature map is much larger than the convolution kernel, resulting in many invalid operations. The overlap addition method is proposed to reduce invalid calculations and speed up network execution better. This work designs a hardware accelerator for frequency domain convolution and verifies its efficiency on the Xilinx Zynq UltraScale+MPSoC ZCU102 board. Comparing the calculation time of visual geometry group 16(VGG16) under the ImageNet dataset faster than the traditional time domain convolution, the hardware acceleration of frequency domain convolution is 8.5 times.

融合快速傅里叶卷积的域变换图像去雨滴方法

在下雨天气中,玻璃上的雨滴会对图像质量产生严重影响,且目前的去雨滴方法过度依赖成对图像,使得无监督图像雨滴去除面临较大挑战。针对这一问题,提出一种域变换图像去雨滴方法。构建域变换网络(DTN),通过有雨与无雨域之间的变换,以无监督的方式实现图像的雨滴去除。同时,通过引入快速傅里叶卷积(FFC)来设计生成网络和判别网络,实现全局与局部特征的信息交互。在FFC中,通过频谱变换(ST)对空间域和频域进行转换,克服传统卷积神经网络(CNN)感受野不足的问题,从而更好地感知细小的雨滴。在2个真实的雨滴测试集上进行去雨滴实验,结果表明,该方法在定量结果和视觉效果上均优于现有的先进方法。与改进前的U-Net+马尔可夫判别网络相比,改进后的该方法在峰值信噪比(PSNR)和结构相似性指数(SSIM)上分别提升3.37 dB和0.0313,并且其能在去除雨滴的同时还原更多的图像纹理细节。

Black-Scholes模型下亚式期权定价的一种快速傅里叶算法

针对几何平均亚式期权,利用快速傅里叶变换方法得到含特征函数的表达式,从而更快速求解亚式期权.对期权价格进行傅里叶变换,得到表达式可以用标的资产价格对数的特征函数来表示,该表达式可以输出期权价格的结果.对其进行离散化处理,再利用快速傅里叶变换来求解,以输出结果.对Black-Scholes模型下的几何亚式期权定价的表达式进行计算,得出其期权定价模型的特征函数,便可以带入快速求解出相应的期权价值.利用Black-Scholes模型在该方法求解的几何平均亚式期权价值与Black-Scholes模型下原始期权价值的数据进行对比,验证了该方法的有效性和高效性.