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Written by Johan Trygg
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In chemistry, as well in other branches of science, there is a steady trend towards the use of more variables (properties) to characterize observations (e.g. samples, molecules, proc-esses). Wavelet analysis and compression, followed by PCA or PLS and their generalizations, form a simple and practical tool, allowing computations to be made using a much-reduced set of variables, but without any loss of information.
Results can be interpreted in the original variable space, using the inverse wavelet transform on resultant model parameters such as loadings. Additionally, the time- frequency nature of many types of signals can facilitate separation of different physico-chemical features, thus increasing the detection limit and improving fault detection. To best describe the Wavelet transform, let's first take a look at the Fourier Transform and related transforms. As we shall see, the Wavelet transform nicely complements the Fourier transform.
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Tutorial 
