Shao X, Pang C, Su Q
Department of Chemistry, University of Science and Technology of China, P.R. China.
Fresenius J Anal Chem. 2000 Jul;367(6):525-9. doi: 10.1007/s002160000404.
A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods--the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method--were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3.3H2O and PrCl3.6H2O were obtained using the proposed CWT method; the results are satisfactory.
提出了一种基于连续小波变换（CWT）的新方法，该方法使用哈尔小波函数对解析信号进行近似导数计算，并成功应用于光声信号处理。通过对信号应用n次小波变换，可以得到解析信号的近似n阶导数。将从其他四种不同方法——传统数值微分法、傅里叶变换法、萨维茨基-戈莱法和离散小波变换（DWT）法——得到的结果与所提出的CWT方法进行了比较；结果表明，对于无噪声信号，所有结果几乎相同，但对于有噪声信号，所提出的CWT方法优于前四种方法。使用所提出的CWT方法获得了Pr（Gly）3Cl3·3H2O和PrCl3·6H2O光声光谱的近似一阶和二阶导数；结果令人满意。
