 At the end of the course:
 the student can evaluate the data from Fourier based analytical methods (FTIR, NMR, MRI, FTMS (ICR) and crystallography).
 the student is able to define acquisition parameters of the main Fourierbased 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.

 Fourier analysis is of great importance 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 behind the Fourier transform and how to use it. The power of this methodology will be demonstrated by discussing its application in Spectroscopy, Imaging and Xray diffraction. During the computer practicals processing of various signals will be exercised using the Matlab computing environment. 



Necessary: • J. Kauppinen, J. Partanen, Fourier Transforms in Spectroscopy • A.P.M. Kentgens, synopsis The Fourier transformation in chemistry Additional recommended literature: • J.F. James, A student’s guide to Fourier transforms • R.N. Bracewell, The Fourier transform and its applications 
• 16 hours computer course • 16 hours lecture • 16 hours problem session 
This course will be taught in Dutch 
The following subjects are part of the course: • Fourier series and Fourier synthesis • (Complex) Fourier integrals • Wellknown Fourier pairs • General properties of the Fourier transform (Fourier theorems) • Fraunhofer diffraction • Discrete Fourier Transform • Apodization, filtering and phasing of signals • Fourier Transforms in optical spectroscopy (FTIR), NMR spectroscopy and MRI, mass spectrometry (FTMS) and crystallography 
The assessment is based on a written test (60%) and the reports of the commands in the computer practicals (40%). For the computer practicum is a mandatory presence. With the return of the seminar contents is to earn a bonus. 
Linear Algebra (NWIMOL016), Programming in Matlab (NWIMOL033). This is a course in the theme 'Methods'. 
  Required materialsBookJ. Kauppinen, J. Partanen, Fourier Transforms in Spectroscopy 
 ReaderA.P.M. Kentgens, synopsis The Fourier Transform in chemistry 

 Recommended materialsBookJ.F. James, A student’s guide to Fourier transforms 
 BookR.N. Bracewell, The Fourier transform and its applications 

 Instructional modesLecture
 Practical computer trainingAttendance Mandatory   Yes 
 Tutorial

 TestsTentamenTest weight   1 
Opportunities   Block KW3, Block KW4 


 