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 about frequency changes over time and the short time Fourier transform (STFT) technique was suggested as a solution to this problem. The wavelet transform has similarities to STFT, but partitions the time-frequency space differently in order to obtain better resolutions along time and frequency/scales. In STFT a constant bandwidth partitioning is performed whereas in the wavelet transform the time-frequency domain is partitioned according to a constant relative bandwidth scheme. In this paper we also discuss the following application areas of wavelet transforms in chemistry and analytical biotechnology: denoising, removal of baselines, determination of zero crossings of higher derivatives, signal compression and wavelet preprocessing in partial least squares (PLS) regression.