In this paper, taking the downward continuation of potential field as an inverse problem of upward continuation, we obtain a convolution type linear integral equation for downward continuation. Making use of the orthogonal symmetry characteristic of Fourier transform matrix, and combining the principles of singular value decomposition of matrix and generalized inverse, we proposed a stable generalized inverse method for downward continuation of potential field, called wavenumber domain generalized inverse algorithm, which doesn't need the computation for inverse matrix. It resolves the instability of potential field downward continuation of large depth.
本文通过把位场向下延拓视为向上延拓的反问题，得到向下延拓的褶积型线性积分方程，再利用Fourier变换矩阵的正交对称特性，并结合矩阵的奇异值分解和广义逆原理，提出了一种稳定的不需要进行求逆运算的位场向下延拓广义逆方法——波数域广义逆算法，解决了位场大深度向下延拓的不稳定性问题。
Then is the property of fourier transform detally, it contains linar, symmetry, uncover, switch, time-move, frequency-move, time-differentialcoefficient, frequency-differential coefficient, time-intergrate, frequency-intergrate, odd even, theorem of Parseval, and theorem of convolution, and make testify to some property, some have the example.
接着详细概括了傅立叶变换的性质，即线性、对称性、折叠性、尺度变换性、时移性、频移性、时域微分性、频域微分性、时域积分性、频域积分性、帕塞瓦尔定理、奇偶性及卷积定理等，对某些性质相应的做了推导，并附有适当事例。
Based on Fresnel-Kirchhoff diffraction theory, taking the clinical conditions of the amplitude approximation and the moderate variation condition for phases into account, the image intensity formulas of micro-focus X-PCI in the range of focal aperture on the image plane are derived by Fourier transform and the convolution theorems.
根据Fresnel-Kirchhoff衍射理论，结合临床实际，考虑振幅近似和相位缓变条件，由傅里叶变换和卷积定理，导出了微聚焦X射线相衬成像（X-ray Phase-contrast Imaging，X-PCI）在像平面上焦斑尺寸范围内的能量密度分布函数。
We implement the algorithm of discrete wavelet transform with two ways based on short-length FIR filtering algorithm and circular convolution respectively, the analysis of computation of the two methods are described. An algorithm of fast wavelet decomposition based on properties of Shannon wavelet is proposed.
研究了用循环卷积和基于短FIR滤波器结构实现离散小波变换的计算量问题；在对香农小波的多分辨分析作了较深入研究的基础上，提出了一个基于香农小波的快速分解方法。
By virtue of inverse Fourier transform and convolution theorem, a semi-analytical solution for the velocity response of a pile subjected to a semi-sine wave exciting torque is obtained in the time domain.
进一步根据桩土接触面上的位移、应力连续条件，求解了桩身动力平衡方程，在频域内得到了桩顶动力响应的解析解。
Chapter 2 introduces the basic theory of image enhancement, convolution theorem and Fourier transform.
第二章先介绍了图像增强的基本理论，卷积定理以及傅里叶变换。
From the most basic signal analysis, digital signal processing, and the Fourier transform convolution theorem was derived and that, and with MATLAB simulation.
本文从最基本的信号系统分析、数字信号处理过程开始，对傅里叶变换以及卷积定理进行了推导和证明，并且用MATLAB进行仿真。
This article from the start with the basic signal analysis, the Fourier transform, convolution theorem derivation and feasibility studies, and its use of simulation software MATLAB simulation, to be more intuitive signal of the spectrum changes, simulation discrete signal The system response.
本文就从最基本的信号系统分析入手，对傅里叶变换、卷积定理进行推导和论证，并且运用仿真软件MATLAB对其进行仿真，目的是更直观的研究信号的频谱变化关系，仿真离散信号的系统响应。
There are additional two outputs through the study of edge detection in image fusion. One is a method of extracting coastline in SAR images by improvement of maximum edge detection, the other is research on application of Bubble wavelet in zero-across edge detection and points out some mistakes concerning application of the wavelet in multi-resolution analysis in some literatures. The Mexico hat wavelet is only used for Continues Wavelet Transform. The technique providing approximate template for continues convolution and how it used for zero-crossing edge detection are also provided.
作为研究边缘检测图像融合的副产品，还得到了两个附加成果，一是将极大值边缘检测进行一些改进得出了一种用于SAR图像海岸线检测的简易方法；二是研究了Bubble小波在跨零点边缘检测时的运用，指出了一些文献中对该小波用于多分辨率分析的错误，指出该小波只能用于连续小波变换，并说明了如何得到连续卷积的近似模板以及用于跨零点边缘检测。
Compared with time-domain interference excision techniques, transform-domain techniques have espial merits such as the convolution operation in time-domain can be realized in transformdomain by multiplication operation.
相对时域抗干扰技术而言，变换域抗干扰技术具有独特的优点，如在时域中的卷积运算在变换域中可以用简单的相乘来实现。
By means of the orthogonal transform and its fast algorithm, the generalized discrete convolution method is presented in this paper under the condition of minimal Frobenius norm of the iterative operator.
利用正交变换及其快速算法，以迭代算子的Frobenius范数最小为准则，推广了求解电大尺寸电磁场问题的离散卷积法和修正离散卷积法，提出了一类迭代法，即广义离散卷积法。
One way of using Linear Convolution Transform has been presented to improve the accuracy.
文中提出采用线性调频Z变换的方法来提高时延估计的精度。
An automatic analysis method, which bases on image convolution localizing, Fourier transform and concise cross correlation algorithm, is developed for obtaining droplets'diameters and velocity of spray by using PIV setup. The method is experimentally tested on the water spray generated by an injector, and the different region of the spray is measured.
为了验证该方法的测量精度，对喷嘴生成的气水两相流进行了测量实验，得到了喷嘴出口处不同区域的粒径、速度矢量的空间分布，并将测得的速度矢量与用粒子成像测量技术方法测得的结果进行对比，证明两种方法测量的平均速度差别仅为0.38％。
The high frequency signals and noise signals are first decomposed into three different directions by making use of the 2-dimensional Daubechies wavelet transform to process matrix data with row convolution and line convolution.
利用二维db小波变换对矩阵数据分别进行行卷积和列卷积，把检测数据的高频信号和噪声信号分解在3个不同的方向上，且信号的能量集中在很少的小波系数上。
On the basis of comprehensive researches of the existing Gaussian filtering method for surface roughness, the convolution algorithm and fast Fourier transform algorithm for the Gaussian regression filter and Gaussian robust filter have been deduced and the C codes have been programmed.
在讨论现有表面粗糙度高斯滤波方法的优缺点的基础上，推导了高斯回归滤波及高斯稳健滤波的卷积算法和快速傅里叶算法过程，编写了算法的C语言代码。
In this paper, we discussed a two-variable cyclic convolution algorithm based on two-variable polynomial multiplication, and compared it with the fast polynomial transform (FPT) algorithm. As a result, this kind of algorithm is efficient in computation of two-variable cyclic convolutions.
本文详细讨论一种基于多元多项式乘积的二维循环卷积算法，并与其快速多项式变换（FPT）算法进行了比较，比较结果显示该算法具有明显的优越性。
Achieving particle location by convolution, extracting the interference fringe information from the Fourier transform frequency spectrum chart of the particle image, the size of particle was calculated by the formula using the data mentioned above.
采用卷积方法实现粒子定位，从粒子图像傅立叶变换频谱图中提取其干涉条纹信息，代入测量公式求得粒子直径。
Further, in combination with the plane strain model, the analytical solutions of longitudinal vibration response of piles in frequency domain and the corresponding semi-analytical solutions in time domain were obtained using Laplace transform and convolution theorem.
进一步结合平面应变模型，通过Laplace变换和卷积定理等数学方法，求得任意激振力作用下的桩体振动频域响应解析解和时域响应半解析解。
A Digital Circular Convolution Algorithm by Radix 2 Polynomial Transform
基2的多项式变换求循环卷积的算法
So that the discrete Gyrator transform can be calculated by the Fast Fourier transform. The convolution expression of the general linear canonical transform has been derived. So it can be calculated by the Fourier transform according to the convolution theorem of Fourier transform.
其次，推导了一般线性正则变换的卷积表达形式，根据傅里叶变换的卷积定理，由快速傅里叶变换实现卷积计算。