An efficient recursive algorithm for time-varying Fourier transform

An efficient recursive algorithm for computing the time-varying Fourier transform (TVFT) or short-time Fourier transform (STFT) of a time sequence is presented. In this approach, instead of excluding the old samples, their importance is diminished by using all-pole moving windows. This recursive algorithm requires about one half of the computation and storage of the Amin's algorithm. The resulting TVFT does not possess any sidelobes. The performance of the algorithm is illustrated by two numerical examples     

Efficient algorithm for 2-D arithmetic Fourier transform

This article presents an efficient algorithm for the two-dimensional (2-D) arithmetic Fourier transform (AFT) based on the Mobius inversion formula of odd number series. It requires fewer multiplications and has less complexity over previous algorithms. In addition, a technique is proposed to carry out the on-axis Fourier coefficients. A parallel VLSI architecture is developed for the new algorithm     

FTIR光谱仪中傅里叶插值采样方法的研究

为解决传统Brault采样方法中参考信号过零点计算复杂、耗时较多的问题,提出了基于傅里叶插值技术寻找过零点的方法。通过与其他插值方法进行比较研究,结果表明,这种方法确保了过零点信息准确性的同时简化了数据处理的复杂度,得到的过零点信息线性拟合系数大于0.999。在2 100~2 200 cm-1波段范围内,当参考激光信号误差较小时,傅里叶插值方法得到的仪器SNR是三次样条插值法所得到的1.03倍,而线性插值方法与傅里叶插值方法得到的结果一致;当参考激光信号误差较大时,傅里叶插值方法得到的仪器SNR是线性插值方法得到的仪器SNR的1.05倍。     

Computationally efficient systolic architecture for computing the discrete Fourier transform

A new high-performance systolic architecture for calculating the discrete Fourier transform (DFT) is described which is based on two levels of transform factorization. One level uses an index remapping that converts the direct transform into structured sets of arithmetically simple four-point transforms. Another level adds a row/column decomposition of the DFT. The architecture supports transform lengths that are not powers of two or based on products of coprime numbers. Compared to previous systolic implementations, the architecture is computationally more efficient and uses less hardware. It provides low latency as well as high throughput, and can do both one- and two-dimensional DFTs. An automated computer-aided design tool was used to find latency and throughput optimal designs that matched the target field programmable gate array structure and functionality.     

Computationally efficient discrete cosine transform algorithm

An algorithm is developed for evaluating the discrete cosine transform using DFT and polynomial transforms. It is shown to be computationally more efficient than existing algorithms.     

An efficient coding algorithm for the compression of ECG signals using the wavelet transform

A wavelet-based electrocardiogram (ECG) data compression algorithm is proposed in this paper. The ECG signal is first preprocessed, the discrete wavelet transform (DWT) is then applied to the preprocessed signal. Preprocessing guarantees that the magnitudes of the wavelet coefficients be less than one, and reduces the reconstruction errors near both ends of the compressed signal. The DWT coefficients are divided into three groups, each group is thresholded using a threshold based on a desired energy packing efficiency. A binary significance map is then generated by scanning the wavelet decomposition coefficients and outputting a binary one if the scanned coefficient is significant, and a binary zero if it is insignificant. Compression is achieved by 1) using a variable length code based on run length encoding to compress the significance map and 2) using direct binary representation for representing the significant coefficients. The ability of the coding algorithm to compress ECG signals is investigated, the results were obtained by compressing and decompressing the test signals. The proposed algorithm is compared with direct-based and wavelet-based compression algorithms and showed superior performance. A compression ratio of 24:1 was achieved for MIT-BIH record 117 with a percent root mean square difference as low as 1.08%.     

滑动离散傅里叶算法输出稳定性研究

受数字系统有限字长的影响,滑动离散傅里叶变换(滑动DFT)算法的频率单元存在输出不稳定的缺点。利用改进Goertzel算法的递归单元对滑动DFT算法的频率单元改造后,不仅可以直接计算起始频谱值,而且滑动DFT算法可以每隔N个输出值就对频率单元清零,并能提供准确的新谱值,保证了滑动DFT算法的频率单元可以长时间连续不断的处理输入数据,而不会出现输出不稳定现象。这种方法在连续地、实时地进行时频谱分析中具有重要的意义。     

基于分数阶傅里叶变换的运动舰船聚焦算法

为解决合成孔径雷达(SAR)图像中运动舰船目标产生的散焦现象,结合对比度最大算法和分数阶傅里叶变换(FRFT)算法,提出了一种改进的对比度分数阶傅里叶变换(CFRFT)自聚焦算法.该算法利用分数阶傅里叶变换对已成像SAR图像进行时频域分析,根据旋转角分别利用参数模型和非参数模型对二阶相位误差和高阶相位误差进行补偿,和传统的相位梯度(PGA)法相比,图像分辨率和旁瓣比提升显著,可以更有效地补偿SAR中舰船运动产生的相位误差.对不同舰船和尾迹SAR图像实验表明,算法对二阶以上的相位误差具有较好的补偿效果,误差估计准确性高,适用范围广,解决了SAR运动舰船的散焦问题,提高了海洋舰船监测的准确性.     

一种基于Fourier变换的人脸识别算法

针对现有的多数人脸识别算法在单训练样本时识 别性能并不理想这一问题,提出一种基于Fourier-Mellin变换的频域不 变性以及时域不变性的特征提取算法。首先,采用图像亮度作为原始特征,将对图像亮度标 准化以改善光照变化,通过应用2D小波变换降维来管理频域不变量的复杂度;然后,为进一 步改进识别性能,根据分析的Fourier-Mellien变换(AFMT) 以及正交Fourier-Mellin矩(OFMM)法不变量的特征,将两种算法混合,进行特征提取; 最后,利用分值标准化度量频域不变量与时域不变量,并存储到一个特征向量中用于分类。 通过最近邻分类器(NNC)和相关性系 数法(CCM)进行分类和融合。通过在YALE与ORL人脸数据库上进行了大量实验的结果表明, 本文提出方法的性能要优于传统的人脸识别算法。     

一种改进的消零频傅里叶变换轮廓术

为提高傅里叶变换轮廓术(FTP)的测量精度和范围,提出了一种改进的消零频FTP。将两幅随机相移正弦条纹通过DLP投影仪投射到待测物体上,由CCD相机采集受物体形貌调制的变形光栅条纹图,将采集的两幅条纹图相减得到无零频的条纹差图。对条纹差图进行快速傅里叶变换(FFT)后,通过简易滤波器提取基频成分,将其与彩色条纹或复合光栅投影相结合,可实现单次投影。理论和实验证明了本方法的可行性。     

An accurate error analysis model for fast Fourier transform

An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm. With the model, an accurate error expression and error variance for the computation of FFT are derived. This correspondence deals with fixed-point and block floating-point arithmetic. Simulation results agree closely with the theoretical predicted ones. We find that some roundoff errors at different stages correlate with each other. The density of correlations is closely associated with the round-off approach used in butterfly calculations     

Iterative algorithm for nonuniform inverse fast Fourier transform(NU-IFFT)

A nonuniform inverse fast Fourier transform (NU-IFFT) for nonuniformly sampled data is realised by combining the conjugate-gradient fast Fourier transform (CG-FFT) method with the newly developed nonuniform fast Fourier transform (NUFFT) algorithms. An example application of the algorithm in computational electromagnetics is presented     

Fast hardware implementation of the Winograd Fourier transform algorithm

We describe a novel partitioning of small Winograd DFTs into two identical subunits, each of which computes a real-input DFT. A bit-serial arithmetic single IC implementation in semicustom or custom LSI is described. A fast hardware WFTA is then proposed which is efficient for complex or real input data.     

An efficient pipelined architecture for real-valued Fast Fourier Transform

Real-valued Fast Fourier Transform (FFT) plays an important role in today’s digital world because of the fact that most of the signals contain real values. The FFT computation of real signals using conventional techniques requires more hardware space with high power consumption, which is the most important task for a researcher while designing VLSI architectures. This can be eradicated by clearly analysing the symmetric property of the real-valued signals. In this paper, we have adopted the symmetric property and designed an efficient pipelined architecture for 16-point DIF FFT. The pipeline scheme reduce the processing time at the cost of some registers and in order to contribute efficiently for power reduction we have modified the complex multiplier with reduced internal real multipliers which are in turn replaced by an modified canonic signed digit multiplier (CSDM) with resource-sharing technique. The complete module is synthesised and simulated using Xilinx ISE 14.1 with the target device is Virtex-5 xc5vlx110T. The experimental results verify that our implemented design is more efficient in terms of speed, area and power when comparing with similar works.     

基于双时域傅里叶变换的相位测量算法

提出了一种双时域傅里叶变换相位提取算法。通过把一段具有两个干涉周期的时域光强信号分成多段一个周期的子段,通过两次使用傅里叶变换把相移器引入的相移频率和其他干扰频率分离出来,模拟和实验结果都证明了该算法在不提高系统复杂性和大幅度减少数据获取量的前提下显著提高了系统抗干扰能力,该方法从采集到待测物体相位的提取,完全无须人工干预,有利于实现自动化。     

一种基于分数傅立叶变换的图像加密技术

本文基于分数傅立叶变换的多样性,通过不同级次的分数傅立叶变换与谱变换相结合,提出了一种新的光学图像加密算法。经计算机模拟验证,此算法确实可行可靠。     

海洋合成孔径雷达图像的一种高效压缩方法

针对通用压缩算法未利用合成孔径雷达（SAR）图像特征的不足,提出一种基于概率分布的自适应海洋SAR图像压缩算法。利用海洋SAR图像的概率分布,根据目标的分布设计量化方案,使目标和背景得到不同程度的保留。利用场景的稀疏性,将阈值以上的像素映射到三元组,对其灰度和位置信息分别熵编码;利用剩余背景层灰度偏差较小的特点作位平面编码。实验结果表明,该算法能有效地压缩图像,同码率下峰值信噪比（PSNR）较JPEG2000高5dB～10dB。本文算法复杂度低,对比度保持好,适用于针对不同需求的海面舰船SAR图像压缩。     

An efficient algorithm for two-dimensional frequency estimation

This paper presents a computationally efficient eigenstructure-based 2D-MODE algorithm for two-dimensional frequency estimation. We derive the theoretical performance of the 2D-MODE estimator and show that it is asymptotically statistically efficient under either the assumption that the number of temporal snapshots is large or the signal-to-noise ratio is high. Numerical examples showing the performance of this algorithm and comparing it with the computationally efficient subspace rotation algorithms are also given. We show that the statistical performance of the 2D-MODE algorithm is better than that of the subspace rotation methods. The amount of computations required by the former is no more than a few times of that needed by the latter for either small numbers of spatial measurements or a single temporal snapshot, which are the cases of interest herein.     

一种有效的混合噪声滤波算法

以噪声特点和图像结构分析为基础,提出了一种有效的混合噪声滤除算法。算法首先通过极值判断和像素间的相容性检测,分离出脉冲噪声并以中值滤波滤除;然后对含有高斯噪声的图像以模糊滤波算法进行降噪处理。实验结果表明,本算法能有效地滤除图像中脉冲与高斯混合噪声,且较好地保护了图像细节特征。