基于矩的快速离散余弦变换处理机的设计及实现

阐述了基于矩的离散余弦变换算法和易于ＶＬＳＩ实现的脉动阵列算法结构,然后从软硬件结构划分、电路实现技术等方面探讨离散余弦变换处理机系统的设计思路。最后给出用矩实现的计算框图、电路实现框图以及外围驱动软件的结构设计。     

离散余弦变换的改进的算术傅立叶变换算法

离散余弦变换(DCT)是数字图像处理等许多领域的重要数学工具.本文通过一种新的傅立叶分析技术——算术傅立叶变换(AFT)来计算DCT.本文对偶函数的AFT进行了改进.改进的AFT算法不但把AFT所需样本点数减少了一半,从而使所需加法计算量减少了一半,更重要的是它建立起AFT和DCT的直接联系,因而提供了适合用于计算DCT的AFT算法.本文推导了用改进的AFT计算DCT的算法并对算法进行了简要的分析.这种算法的乘法量仅为O(N),并且具有公式一致,结构简单,易于并行,适合VLSI设计等特点,为DCT的快速计算开辟了新的途径.     

45分钟进入离散傅立叶变换

离散傅立叶变换在数字信号处理课程中非常重要,也非常难,在讲解离散傅立叶变换的公式和性质之前,应先让学生理解离散傅立叶变换的物理意义以及与其他三种傅立叶变换的联系,本文采用3W1H的叙述方式让学生对离散傅立叶变换产生学习兴趣。     

补零离散傅立叶变换的插值算法

插值离散傅立叶变换能提高正弦信号参数估计精度,但传统的比值插值算法只适用于数据长度等于离散傅立叶变换长度的场合。本文研究了补零离散傅立叶变换的插值问题,提出一种基于窗函数频谱一阶泰勒级数展开的插值算法,它与原比值法具有类似的形式和相同的计算量,是原比值法在数据长度小于或等于离散傅立叶变换长度时的扩展。性能分析和仿真试验还表明,补零离散傅立叶变换插值算法对频率偏差的敏感度降低,稳定性更好。     

基于二维离散傅立叶变换的射频信号调制类型识别

针对已有算法应用的局限性．以线性调频．二相编码,频率编码和正弦等典型射频信号为例,提出了一种基于二维离散傅立叶变换的射频信号调制类型识别新算法,重点阐述了信号自相关变换过程和运算量分析．计算机仿真结果验证了本算法确实有效。     

基于离散匹配傅立叶变换的多分量LFM信号检测和参数估计

多分量LFM信号的检测和参数估计是一个被广泛讨论的问题。本文首先介绍了离散匹配傅立叶变换的基本原理,然后结合逐次消去的思想提出了基于离散匹配傅立叶变换的多分量LFM信号检测和参数估计的原理及实现算法,并进行了计算机仿真。仿真结果验证了该算法的有效性。     

离散小波变换的VLSI设计

在本文中，我们提出了一种离散小波变换（DWT）及其逆变换（IDWT）的VLSI结构，这一结构利用DWT／IDWT的结构和数值特性大大降低了系统的实现规模，同时由于采用了并行流水线和平衡数据通道等技术，可以获得每个时钟两个数据的处理速度和五个时钟节拍的流水线时延．基于硬件描述语言VHDL的模拟和综合结果表明，采用1．5μmCMOS工艺时，电路的规模为5058单元面积，在最坏情况下，最高时钟频率约可达55MHz，数据处理速度达到110Mpoints／s．     

基于VC图像离散傅立叶变换研究

本文介绍了傅立叶变换应用和VC图象的处理，以数学为基础的解决方法，通过图象做了比较。     

改进的算术傅立叶变换（AFT）算法

算术傅立叶变换（AFT）是一种非常重要的傅立叶分析技术。AFT的乘法量少（仅为O（N））,算法结构简单,非常适合VLSI设计,具有广泛的应用。但AFT的加法量很大,为O（N∧2）,因此减少AFT的加法运算是很重要的工作。本文通过分析AFT的采样特点,给出了奇函数和偶函数的AFT的改进算法。然后在此基础上给出了一般函数的AFT的改进算法。改进算法比原算法的加法运算量降低了一半,因此计算速度快了一倍。本文改进的偶函数和奇函数的AFT算法还分别可以用来计算离散余弦变换（DCT）和离散正弦变换（DST）。     

基于傅立叶变换的乐音分析和生成

人类听觉能听到乐音、噪音等声音,乐音是一种较和谐的声音。乐音作为一种周期性信号,时时刻刻地存在于人们的生活当中。并且随着计算机的广泛深入应用,通过研究这种信号我们可以合成我们需要的电子音乐等等。在本文中主要分析通过傅立叶方法来研究乐音。对原信号使用离散傅立叶变换研究乐音的组成原理,并运用离散傅立叶逆变换进行音乐的生成。基于傅立叶方法,我们不仅分析音乐的组成,也提出一种利用计算机生成乐音的思路。     

The discrete fractional Fourier transform based on the DFT matrix

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yet-elegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT. By appropriately combining existing commuting matrices we obtain a new commuting matrix which performs better. We show the validity of the proposed algorithms by computer simulations comparing DFrFT points and continuous FrFT samples for various signals.     

The discrete rotational Fourier transform

We define a discrete version of the angular Fourier transform and present the properties of the transform that show it to be a rotation in time-frequency space, this new transform is a generalization of the DFT. Efficient algorithms for its computation can then be based on the FFT and the eigenstructure of the DFT     

The discrete fractional Fourier transform

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The definition is exactly unitary, index additive, and reduces to the DFT for unit order. The fact that this definition satisfies all the desirable properties expected of the discrete fractional Fourier transform supports our confidence that it will be accepted as the definitive definition of this transform     

离散傅里叶变换性质的可视化教学设计

离散傅里叶变换是“数字信号处理”的重要教学内容,然其定义及主要性质涉及大量数学公式推导表征,较为抽象枯燥,不利于学生直观深入理解;且课程内容中对理论知识的具体应用场景涉及较少,难以激发学生的学习兴趣。针对此问题,提出了将数字图像频谱分析作为离散傅里叶变换性质教学的辅助手段,对线性、循环移位、对称性、对偶性等主要性质,分别进行直观形象的可视化展示。课程实践结果表明,该教学设计能有效提高学生的学习兴趣和知识掌握度,取得了较好的教学效果。     

Vectorized mixed radix discrete Fourier transform algorithms

A number of previous attempts at the vectorization of the fast Fourier transform (FFT) algorithm have fallen somewhat short of achieving the full potential speed of vector processors. The algorithm formulation and implementation described here not only achieves full vector utilization but successfully copes with the problems of hierarchical storage. In the present paper, these techniques are described and extended to the general mixed radix algorithms, prime factor algorithm (PFA), the multidimensional discrete Fourier transform (DFT), the rectangular transform convolution algorithms, and the Winograd fast Fourier transform algorithm. Some of the methods were used in the Engineering Scientific Subroutine Library for the IBM 3090 Vector Facility. Using this approach, very good and consistent performance was obtained over a very wide range of transform lengths.     

Source coding of the discrete Fourier transform

Distortion-rate theory is used to derive absolute performance bounds and encoding guidelines for direct fixed-rate minimum mean-square error data compression of the discrete Fourier transform (DFT) of a stationary real or circularly complex sequence. Both real-part-imaginary-part and magnitude-phase-angle encoding are treated. General source coding theorems are proved in order to justify using the optimal test channel transition probability distribution for allocating the information rate among the DFT coefficients and for calculating arbitrary performance measures on actual optimal codes. This technique has yielded a theoretical measure of the relative importance of phase angle over the magnitude in magnitude-phase-angle data compression. The result is that the phase angle must be encoded with 0.954 nats, or 1.37 bits, more rate than the magnitude for rates exceeding 3.0 nats per complex element. This result and the optimal error bounds are compared to empirical results for efficient quantization schemes.     

Binary windows for the discrete Fourier transform

An efficient structure is suggested for the frequency-domain windowing of discrete Fourier transforms. In this scheme, multiplications are replaced by shifts in the position of the binary point. Three new window functions are described which can be realized by the suggested structure.     

Image fusion based on discrete Chebyshev moments

Though deep learning-based methods have demonstrated strong capabilities on image fusion, they usually improve the fusion performance by increasing the width and depth of the network, increasing the computational effort and being unsuitable for industrial applications. In this paper, an end-to-end network based on fixed convolution module of discrete Chebyshev moments is proposed, which does not need any pre- or post-processing. The proposed network is roughly composed of three parts: feature extraction module, fusion module and feature reconstruction module. In the feature extraction module, a novel fixed convolution module based on discrete Chebyshev moments is proposed to obtain different frequency components in a short time. To improve the image sharpness and fuse more details, a spatial attention mechanism based on average gradient is proposed in fusion module. Extensive results demonstrate that the proposed network can achieve remarkable fusion performance, high time efficiency and strong generalization ability.     

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。     

基于离散傅里叶变换的高动态突发信号检测及频率估计

针对高动态突发通信应用环境,提出了一种新的基于频率域的突发信号检测及载波频偏估计算法,通过一次离散傅里叶变换( DFT)实现突发信号存在性检测及频率估计,并与经典Power-Law算法进行了比较。仿真结果表明：在低信噪比条件下,新算法检测信噪比门限改善超过1 dB,频率估计均方根误差小于符号率的1‰,并且对载波频偏及信号电平动态不敏感,实现结构简单,适合实时处理及工程应用。