频率函数

The main work of this paper is to study the sampling theorem in domain of the fraction and the sampling relationship. We will try to obtain the theoretic sampling rate and the proof of feasibility. And we also give some relationship between the kernels under the meaning of sampling.

本文的主要工作就是，研究了分数傅立叶变换算子核函数的采样定理及采样关系，给出了一种能够达到理论的最佳采样频率的尝试，也给出了这种做法的可行性的证明，更进一步由采样关系给出了核函数的一些关系。

For the digital filter design problem, the mathematics are complicated by the approximation being defined on the unit circle.

数学问题中固有的频域滤波器设计的问题是逼近理想的复杂的频率响应函数的HD的一个合理的传递函数的H就一个Mth度的分子和一个第N次度标准值复杂的变量沿着单位圆的Z = ejw 。

The content involves Digital Filter, Auto Correlation, Cross Correlation, mean and standard deviation, probability density and probability distribution statistic, as well as Auto Power Spectrum based on Fast Flourier Transfer, Correct Power Spectrum, Cestrum and Frequency Response. The Short-time Flourier Transfer and Wavelet Transfer are included in the analysis program.

具体内容包括：数字滤波、时域加窗、自相关计算与互相关处理、均值和方差计算、概率密度和概率分布统计，快速傅立叶变换基础上的自功率谱、互功率谱、频率响应函数、相关函数、倒频谱分析；基于短时傅立叶分析的联合时频分析、小波变换等。

The main factors effecting on exploration precision of surface wave are analyzed in the light of calculation of phase velocity of surface wave; the merits and demetits of common computing methods for phase velocity between stations and their applied range are discussed and calculation of interstation Green's function for correcting phase is put forward to get the precise phase difference between two stations.

分析了影响面波勘探精度的主要因素，针对计算面波相速度的精度问题，讨论了常用测量台间面波相速度方法的优缺点及其适用范围，并提出通过测量台间格林函数进行相位校正，以得到两台之间的精确相位。以合成的高频理论地震图作为记录信号，并在理论地震图上叠加了 2 0 %的随机噪声，利用这些方法分析理论信号，数字实验表明：在相干频率范围内，格林函数方法能够精确测量台间相速度，而互相关法和窄带通滤波互相关法所得结果较为离散。

You can see that the smooth noise is flatter, never reaching the extremes of unsmoothed noise, and the frequency appears to be roughly half.

你可以看见平滑函数，从来都没有到底那个未平滑函数的极限值，并且频率显得只有大约一半。

The purpose of this study is to present the characteristics of wavelet functions, to compare the effects of choosing different wavelets on wavelet transform, and to discuss the wave shoaling with the help of he WaveletTransform .

本文主旨在於介绍小波函数的特性并探讨不同小波函数对小波转换的影响，再以此分析工具讨论浅化波浪能量於时间－频率域上之变化特性。

In comparison with the drawbacks related to the Fourier Transform and Smoothed Instantaneous Wave Energy History(SIWEH, the Wavelet Transform will be show to be much better suited for analyzing wave shoaling In which signal is believed to be non-stationary and wide band.

在使用小波转换作为分析波浪工具之前，我们选择 Morlet wavelet、Paul wavelet与Gaussian三种型态之小波函数进行讨论，最终考虑视窗面积之大小、复数型态之小波函数及频率视窗的集中度，而以 Morlet wavelet较适合分析波浪。

More general, spectrum shape was related with the shape of response function, dispersion angle affect the lowest spatial frequency, and color cycle number can modify the distribution of low and high spatial frequency to change the smoothing effect.

一般地，光谱形状控制空间响应函数形状，色散角决定所能匀滑的最低频率，色循环数可改变响应函数特点，调整对空间低频和高频的匀滑效果。

More generally, spectrum shape was related with the shape of response function, the dispersion angle affects the lowest spatial frequency, and color cycle number can modify the distribution of low and high spatial frequency to change the smoothing effect.

一般地，光谱形状控制空间响应函数形状，色散角决定所能匀滑的最低频率，色循环数可改变响应函数特点，调整对空间低频和高频的匀滑效果。

Combined with the boundary conditions of soil surface under unit impulse excitation,the Green's functions for ground displacements in wavenumber-frequency domain are deduced.The Green's functions obtained are implemented by MATLAB,and their preliminary characteristics are presented via an example.

结合单位脉冲荷载作用下地基土表面的边界条件，推导出波数-频率域内地基土表面位移Green函数的解析解，用Matlab程序语言对理论进行实现并通过算例对地基土表面位移Green函数的特征进行了分析和总结。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。