AN INTRODUCTION TO WAVELET TRANSFORMS FOR CHEMOMETRICIANS - A TIME-FREQUENCY APPROACH

One way to obtain an intuitive understanding of the wavelet transform is to explain it in terms of segmentation of the time-frequency/scale domain. The ordinary Fourier transform does not contain information ab out frequency changes over time and the short time Fourier transform ( STFT) technique was suggested as a solution to this problem. The wavel et transform has similarities to STFT, but partitions the time-frequen cy space differently in order to obtain better resolutions along time and frequency/scales. In STFT a constant bandwidth partitioning is per formed whereas in the wavelet transform the time-frequency domain is p artitioned according to a constant relative bandwidth scheme. In this paper we also discuss the following application areas of wavelet trans forms in chemistry and analytical biotechnology: denoising, removal of baselines, determination of zero crossings of higher derivatives, sig nal compression and wavelet preprocessing in partial least squares (PL S) regression.