A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) using Haar wavel et 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 apply ing n times of the wavelet transform to the signal. The results obtained fr om four other different methods - the conventional numerical differentiatio n, the Fourier transform method, the Savitzky-Golay method, and the discret e wavelet transform (DWT) method - were compared with the proposed CWT meth od; it was demonstrated that all the results are almost the same for signal s 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)(3)Cl-3. 3 H2O and PrCl3. 6 H2O were o btained using the proposed CWT method; the results are satisfactory.