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At the end of the course:
- the student can evaluate the data from Fourier based analytical methods (FT-IR, NMR, MRI, FT-MS (ICR) and crystallography).
- the student is able to define acquisition parameters of the main Fourier-based methodologies in chemical analysis.
- the student can evaluate appropriate methods to phase correct and filter raw spectroscopic data and calculate their Fourier transform.
- the student can list a set of functions occurring frequently in physical sciences and their Fourier transforms.
- the student understands the basic mathematical principles of Fourier analysis and the related Fourier theorems.
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Fourier analysis is of great relevance in many applications in natural sciences, as many phenomena and processes are inherently periodic. The Fourier transform is one of the most used mathematical tools for the analysis and interpretation of periodic signals. This course introduces Fourier series and gives an overview of the theory underlying the Fourier transform (FT) and its use. The power of this approach will be demonstrated by discussing the application of the FT in Spectroscopy, Imaging and X-ray diffraction. During the computer labs processing of NMR, IR and MS data will be practised using the Matlab computing environment.
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