与Fourier变换相比，小波变换是空间（时间）和频率的局部变换，因而

与Fourier变换相比，小波变换是空间（时间）和频率的局部变换，因而能有效地从信号中提取信息。通过伸缩和平移等运算功能可对函数或信号进行多尺度的细化分析，解决了Fourier变换不能解决的许多困难问题。小波变换联系了应用数学、物理学、计算机科学、信号与信息处理、图像处理、地震勘探等多个学科。数学家认为，小波分析是一个新的数学分支，它是泛函分析、Fourier分析、样条分析、数值分析的完美结晶；信号和信息处理专家认为，小波分析是时间—尺度分析和多分辨分析的一种新技术，它在信号分析、语音合成、图像识别、计算机视觉、数据压缩、地震勘探、大气与海洋波分析等方面的研究都取得了有科学意义和应用价值的成果。信号分析的主要目的是寻找一种简单有效的信号变换方法，使信号所包含的重要信息能显现出来。小波分析属于信号时频分析的一种，在小波分析出现之前，傅立叶变换是信号处理领域应用最广泛、效果最好的一种分析手段。傅立叶变换是时域到频域互相转化的工具，从物理意义上讲，傅立叶变换的实质是把这个波形分解成不同频率的正弦波的叠加和。正是傅立叶变换的这种重要的物理意义，决定了傅立叶变换在信号分析和信号处理中的独特地位。傅立叶变换用在两个方向上都无限伸展的正弦曲线波作为正交基函数，把周期函数展成傅立叶级数，把非周期函数展成傅立叶积分，利用傅立叶变换对函数作频谱分析，反映了整个信号的时间频谱特性，较好地揭示了平稳信号的特征。
小波变换是一种新的变换分析方法，它继承和发展了短时傅立叶变换局部化的思想，同时又克服了窗口大小不随频率变化等缺点，能够提供一个随频率改变的“时间-频率”窗口，是进行信号时频分析和处理的理想工具。它的主要特点是通过变换能够充分突出问题某些方面的特征，因此，小波变换在许多领域都得到了成功的应用，特别是小波变换的离散数字算法已被广泛用于许多问题的变换研究中。从此，小波变换越来越引起人们的重视，其应用领域来越来越广泛。

結果 (英文) 1:

Compared with the Fourier transform, wavelet transform space (time) and frequency of local transformations, which can effectively extract information from the signal. By scale computing features such as panning function or signal can be more refined analysis of the scale, to solve the Fourier transform does not resolve many of the difficult issues. Contact Wavelet transform applied mathematics, physics, computer science, signal and information processing, image processing, seismic, and other disciplines. Mathematicians believe that Wavelet analysis is a new branch of mathematics, it is the functional analysis, Fourier analysis, pattern analysis, numerical analysis of perfect crystals;Signal and information processing experts believe that is time-scale analysis of wavelet analysis and Multiresolution analysis of a new technology, signal processing, speech synthesis, image recognition, computer vision, data compression, seismic, atmospheric and ocean wave analysis research has scientific significance and practical value of the results achieved. Signals the main purpose of the analysis is to find a simple and effective signal transform methods, enable signal contains important information to emerge. Belonging to signal time-frequency analysis and Wavelet analysis, wavelet analysis prior to Fourier transform is the most widely used in the field of signal processing,An analytic tool works best. Fourier transform of the time domain to the frequency domain transform tool in the physical sense, the Fourier transform is the essence of the waveform is decomposed into a superposition of sine waves at different frequencies and. It is important physical meaning of Fourier Transforms, determine the Fourier transform's unique position in signal analysis and signal processing. Fourier transform stretch infinitely in two directions of sinusoidal wave as an orthogonal basis function, periodic function into Fourier series exhibition, exhibition of non-periodic function into Fourier integrals, Fourier transform spectral analysis of the function,Reflects the whole of the signal spectrum characteristics, better revealing the characteristics of stationary signals.
Wavelet transform analysis method is a new, inherited and developed the short-time Fourier transform local ideas, window size does not change the frequency while overcoming shortcomings, is able to provide a change in the frequency of "time-frequency" window is ideal for signal time-frequency analysis and processing tools. Its main characteristics are transformed to fully highlight the characteristics of certain aspects of the question, therefore, the wavelet transform has been applied successfully in many areas,In particular the number of Discrete Wavelet transform algorithm has been widely used in many of the changing research. Since then, the wavelet transform has attracted people's attention, its field of application to more and more widely.

結果 (英文) 2:

Compared with the Fourier transform, wavelet transform is a spatial (time) and the frequency of the local transformation, which can efficiently extract information from the signal. Function or signal can be analyzed by multi-scale refinement of arithmetic functions such as scaling and translation, to solve many difficult problems can not be resolved Fourier transform. Contact wavelet transform multiple disciplines applied mathematics, physics, computer science, signal and information processing, image processing, seismic exploration. Mathematicians believe that Wavelet analysis is a new branch of mathematics, which is the functional analysis, Fourier analysis, spline analysis, numerical analysis of the perfect crystal; signal and information processing experts believe that wavelet analysis is the time - scale analysis and multi-resolution analysis a new technology, it is a signal analysis, speech synthesis, image recognition, computer vision, data compression, seismic exploration, atmosphere and ocean wave analysis and other aspects have made ​​scientific significance and value of the results. The main purpose of signal analysis is to find a simple and effective method for signal conversion, signal contains important information that can be revealed. Wavelet analysis is a part of the signal frequency analysis, wavelet analysis appeared before the Fourier transform is the most widely used signal processing applications, the best means of an analysis of the effect. Fourier transform the time domain to the frequency domain tools interchangeable from the physical sense, the substance of the Fourier transform of this waveform is decomposed into a superposition of sine waves of different frequencies and. This important physical significance is the Fourier transform, Fourier transform determines the signal analysis and signal processing in a unique position. Fourier transform sine wave curve to infinity in both directions of stretching as the orthogonal basis functions, the periodic function to Fourier series development, the development of a non-periodic function Fourier integral, as a function of Fourier transform spectral analysis reflects the time for the entire spectrum of the signal characteristics, to better reveal the characteristics of stationary signals.
Wavelet transform is a new transformation analysis, it inherited and developed the short-time Fourier transform localized thinking, while overcoming the window size does not vary with frequency and other shortcomings, with the frequency change can provide a "time - frequency" window , when the signal frequency is the ideal tool for analyzing and processing. Its main feature is able to fully highlight the issue by changing certain aspects of the characteristics, therefore, the wavelet transform in many areas have been successfully applied, especially discrete wavelet transform digital algorithm has been widely used to transform the study of many problems in . Since then, the wavelet transform more and more people's attention, and its applications to more widely.

結果 (英文) 3:

Compared with the Fourier transform, wavelet transform is the space (time) and frequency of the local transformation, which can effectively extract information from signal. Detailed analysis through dilation and translation can be carried out on multi-scale function or signal, solves many difficult problems cannot be solved by Fourier transform. Wavelet transform with multiple disciplines of Applied Mathematics, physics, computer science, signal and information processing, image processing, seismic exploration. Mathematicians think, wavelet analysis is a new branch of mathematics, it is the functional analysis, Fourier analysis, spline analysis, numerical analysis of the perfect crystal;Signal and information processing expert thinks, wavelet analysis is a time scale analysis and multiresolution analysis, a new technology, it in signal analysis, speech synthesis, image recognition, computer vision, data compression, seismic exploration, atmospheric and ocean wave analysis are made with scientific significance and the application value of the results. The main purpose of signal analysis is to find a simple and effective method of signal transformation, so that the important information contained in the signal can be shown. Wavelet analysis is a kind of time-frequency analysis, in before the advent of wavelet analysis, Fu Liye transform is widely used in the field of signal processing,An analytical method for best results. Fu Liye transform is the time domain to the frequency domain transform into each other tools, from the physical sense, the essence of Fu Liye transform is that the waveform is decomposed into different frequency sine wave superposition and. It is the Fu Liye transform the physical significance, which determines the unique position of Fu Liye transform in digital signal processing and analysis. Fu Liye transform by using sine curve in two directions are unlimited extension of the wave as the orthogonal basis function, periodic function into Fu Liye series, the non periodic function into Fu Liye integral, analyze the frequency spectrum of the function using Fu Liye transform,Reflects the time spectrum characteristics of the signal, which shows the characteristics of stationary signal.
the wavelet transform is a new transform method, it has inherited and developed the short-time Fu Liye transform local theory, at the same time, but also overcome the shortcomings of the window size does not vary with frequency change, able to provide a "time - frequency" change with frequency window, is the ideal tool for time-frequency analysis and processing of signal. Its main characteristic is that the image can be prominent features, some parts of the problem so, wavelet transform has been applied successfully in many fields,Especially the discrete wavelet transform algorithm has been widely used to transform in study of many problems. Since then, the wavelet transform has attracted people's attention, its application field is more widely.