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 Brune ω~2 source spectrum, Hanks and McGuire deduced a simplified formula of RMS accelera- tion by stationary random vibration theory and Parseval theorem.
Hanks 和 McGuire 基于 Brune 的ω~2震源谱，借助平稳随机振动理论和 Parseval 定理给出了估计均方根加速度衰减关系的表达式。
Based on the error-correcting formula and Parseval theorem, uncertainty analysis method of the results emerged, from curve-fit method is studied as a key issue.
针对数据采集卡和曲线拟合引入的不确定度难于分析求解的问题，基于失真度测量的误差修正公式和Parseval定理，重点研究了曲线拟合法失真度测量结果的不确定度分析方法。
Under the condition that the energy weight coefficients are equal, Parseval theorem is applied to prove that GEI can be simplified to TQI, which is also verified through field data of track irregularity.
在能量权系数相同的情况下，利用离散Parseval定理证明广义能量指标可简化成轨道质量指数，并通过实测的轨道不平顺数据验证这一结论。
Based on this iterative method, dynamic power consumption of clock networks was approximated by the summation of the first Fourier-series based terms according to Parseval`s theorem.
在此迭代算法基础上，根据帕斯瓦尔定理该模型用有限阶傅立叶级数项来逼近时钟线网的动态功耗。
According to Parseval's theorem, the MSE in the pixel domain is equivalent to the mean square quantization error in the DCT domain because DCT is a normalized orthogonal transformation.
Parsval's原理指出，图像压缩前、后像素值的均方误差值等同与图像压缩前、后DCT系数的均方误差值，根据这一思想计了JPEG图像无参考客观质量评价算法。
In disturbance detection module, the detection of various disturbances is implemented by adaptive linear neuron and the detected disturbance signals are sent into classification module; by use of discrete wavelet multi-resolution analysis and Parseval`s theorem the energy distribution features under different scales are extracted, meanwhile by use of fractal geometry the local variance dimensions are extracted; combining these two items, the characteristic vector of disturbance signal is composed.
在扰动检测模块中，采用自适应线性神经元实现了对各种扰动的检测，将检测出的扰动信号送入分类模块，采用离散小波多分辨率分析提取不同尺度下的能量分布特征，同时采用分形几何学提取局部方差维数，将二者结合共同构成扰动信号的特征矢量。
An ultrashort pulsed-laser beam is composed of a series of monochromatic continuous waves. According to Parseval theorem, the time-averaged intensity can be calculated by the sum of the intensity of these monochromatic continuous waves. Then we derive an equation to study Talbot effect of a grating illuminated by an ultrashort pulsed-laser beam.
我们采用了频谱分析法，即把超短脉冲光波看成是由一系列的单色光波组成，根据Parseval定理，光栅Fresnel衍射的平均光强由一系列的单色光波的衍射光强之和而求得，这样我们给出了一种分析光栅在超短脉冲光波照射下泰伯效应特性的方法。
The authors investigate the Fourier series of Weyl almost periodic functions by the new definition and prove the Parseval's equality.
通过新形式的定义研究范尔概周期函数的傅立叶级数和帕塞瓦尔等式。
By means of infinite series and Parseval equation, a method for calculating a class of generalized integral has been devised and a precise value of generalized integral derived.
运用无穷级数和Parseval等式，给出了一类广义积分的计算方法，并导出了一个广义积分精确值，同时得出了几个常见正项级数的和。
In virtue of Laplace transform and Parseval equation, the global stability, error estimate is given.
借助于Laplace变换及Parseval等式，给出了全局稳定性的证明、误差估计及全局收敛性的结果。
At first, it briefly states the theoretical bases of frequency-domain technique-Parseval's theorem and optimization theorem, then classical root-square locus method and the advanced contributions to frequency-domain technique are discussed.
首先简述频域法的理论基础：Parseval定理和最佳化定理。然后分别介绍古典根方轨迹法以及频域法的各项现代成果。
Parseval Theorem in the Application of Solving the Generalized Integrals
Parseval定理在广义积分中的应用
In this paper discrete Parseval theorem and sample theorem of Hankel transform are given analytically which are regarded as the extension of quasi-discrete Hankel transform to high order case.
从理论上给出了高阶Hankel变换的离散Parseval定理和抽样定理的表达式，从而为把准离散Hankel变换扩展到高阶情形打下了基础。
Based on the error-correcting formula and Parseval theorem, uncertainty analysis method of the results emerged. from curve-fit method is studied as a key issue.
针对数据采集卡和曲线拟合引入的不确定度难于分析求解的问题，基于失真度测量的误差修正公式和Parseval定理，重点研究了曲线拟合法失真度测量结果的不确定度分析方法。
In the paper the displacement response of a beam & a function of both time and coordinate is convered into a function of time only by means of Parseval's equation.
首先将梁的响应&一个关于时间和坐标的函数，由Parseval等式得到了一个仅关于时间的函数。
A fundamental identity for Parseval frames of subspaces
子空间Parseval框架的一个基本恒等式
In virtue of Laplace transorm and Parseval equation, the global stability is proved.
借助于Laplace变换及Parseval等式，得到了全局稳定性的证明。
Parseval Frame Multiresolution Analysis
Parseval框架多分辨分析
The frame is a special Bessel sequence, which extends the Parseval equality of orthonormal basis in Hilbert space to the two-sided inequality in general sequence.
框架是一类特殊的Bessel序列，框架是把Hilbert空间中的规范正交基满足的Parseval等式推广到比较一般的序列所满足的双边不等式的结果。