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1. Introduction
The wavelet transform WT has attracted recent interest in applied mathematics for signal and image wx processing 1 . This new mathematical technique has been demonstrated to be fast in computation with localization and quick decay properties in contrast to existing popular methods, especially, the fast Fourier. transform FFT . Theory of the WT was developed wx extensively in 1980s 2 . It may be viewed as a synthesis of ideas originating from engineering sub-band coding , physics coherent states and renormalization group and pure mathematics study of Calderon. Zygmund operators . WT became a tool widely used for signal analysis. From 1989 onwards, the WT has been applied for signal processing in chemical stud-ies owing to its efficiency, large number of basis functions available, and high speed in data treatment.

1。引言

小波变换已吸引了最近的兴趣在应用数学信号和图像Wx处理1。这个新的数学技术已被证明是快速定位，与现有的流行的方法，特别是快速衰减特性计算，快速傅立叶。变换。小波理论是20世纪80年代的2个Wx广泛发育。它可以被看作是一种合成子带编码的思想来源于工程，物理相干态和重整化群和卡尔德隆的纯数学的研究。Zygmund算子。重量成为一种广泛使用的信号分析工具。从1989起，WT已经应用在化学研究由于其效率的信号处理，提供大量的基础功能，和高速数据处理。

One of the main features of WT is that it may de-compose a signal directly according to the frequency and represent it in the frequency domain distribution state in the time domain. In the transformation, both time and frequency information of the signal are re-tained. In chemical studies, the time domain can be replaced by other domains such as wavelength. With proper identification of the scales with frequency, higher frequency signals can be separated from the lower one, in the sense that it has zoom-in and zoom-out capability at any frequency. Since WT can focus on any small part of a signal, it has been called wx a mathematical microscope 3 . Another feature of WT is that the development of signals in the fre-quency domain can be constituted with a flexible choice of waveforms rather than with only trigono-metric ones as a basis. For instance, in FFT, only the sine and cosine functions can be chosen as the basis.

In contrast, a lot of such functions can be selected in WT. Therefore, WT is a more powerful method to depict relationships among different variables. Since 1989, more than 70 papers Table 1 have been published by applying wavelet transform in the chemistry literature. In analytical chemistry, applica-tions of WT can be found in the following areas: flow . injection analysis FIA , high performance liquid chromatography HPLC , infrared IR spectrometry, mass spectrometry MS , nuclear magnetic resonance NMR spectrometry, ultraviolet–visible UV–VIS
spectrometry and voltammetry. Besides, WT has also been employed in studying quantum chemistry and chemical physics. In this paper, research works on the applications of WT in chemical studies as mentioned above are reviewed. Research works on WT by Chinese researchers in China are also included Appen-. dix A . Since most papers published in China were written in Chinese, this review provides more infor-mation on their works.

2. Theory of the wavelet transform
A wavelet transform involves the decomposition of a signal function or vector e.g., a spectrum of a chemical into simpler, fixed building blocks at di本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。