傅里叶变换与小波分析的对比研究

The Comparative Study of Fourier Transform and Wavelet Analysis

小波是近十几年才发展起来并迅速应用到图像处理和语音分析等众多领域的一种数学工具,是继110多年前的傅立叶(Joseph Fourier)分析之后的一个重大突破,无论是对古老的自然学科还是对新兴的高新技术应用学科都产生了强烈冲击。本文先简单回顾傅里叶变换讨论其优缺点,然后讨论如何克服其缺点和引入窗口傅里叶变换,继而引入小波的基本概念,重点探讨在大多数情况下小波变换优于傅里叶变换的内在原因。

Wavelet analysis,the mathmatical tool which has been developing in recent decades and are applied in many feilds like image processing and voice analysis etc., is a great breakthrough after the analytic method of Joseph Fourier 110 years ago.It bring about great impact on both triditional natural sciences and some new high-tech application technologies.In the following pages, I shall first give an review on fourier transformation.after that,we talk about the way we overcome its weakness and introduce the basic concepts of wavelet,followed by the introduction of window fourier transformation. The key point of this page is finding the internal reason why wavelet is better than fourier transformation under many situations.