Department of Chemistry and Biochemistry, University of Texas at Arlington, Arlington, TX, USA.
Department of Chemistry and Biochemistry, University of Maryland at College Park, College Park, MD, USA.
J Sep Sci. 2020 May;43(9-10):1998-2010. doi: 10.1002/jssc.202000013. Epub 2020 Mar 19.
Wavelet transform is a versatile time-frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high-performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal-to-noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal-to-noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research.
小波变换是一种通用的时频分析技术，它可以在时间或空间上定位有用信号，并将其与噪声分离。任何分析仪器的检测器输出在数学上等同于数字图像。在时间上（例如高效液相色谱法）或空间上（例如平面色谱法）变化的化学分离中获得的信号适用于小波分析。本文概述了小波分析，并以图形方式解释了所有相关概念。连续小波变换和离散小波变换的概念及其色谱应用以图形方式进行了说明。本文展示了一个使用连续小波变换在噪声色谱图中定性检测重叠峰的示例。对离散小波变换中的信号分解、去噪和信号重建的概念进行了图形讨论。目前色谱仪中使用的所有数字滤波器都有可能展宽和扭曲窄峰。最后，使用该程序对低信噪比色谱图进行了去噪。结果表明，小波分析可使信噪比提高 10 倍以上。具有良好准确性的初始不可见峰被恢复。由于离散小波变换去噪分析适用于分离科学中使用的任何检测器，因此研究人员应该强烈考虑在研究中使用小波。
