General information 
Course unit name: Applied Harmonic Analysis
Course unit code: 568183
Academic year: 20182019
Coordinator: F. Javier Soria de Diego
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture 
30 

 Lecture with practical component 
15 

 Laboratory session 
15 
Supervised project 
20 
Independent learning 
70 
Recommendations 
Further recommendations

Competences to be gained during study 

Learning objectives 
Referring to knowledge

Teaching blocks 
1. Fourier Series; Orthonormal basis and L2 theory; Convergence of the series
2. Fourier transform in Lp; Sampling theorem
3. Maximal operators; Almost everywhere convergence
4. Marcinkiewicz Theorem; Interpolation Theory
5. Convolution operators; Fourier multipliers; Hilbert transform
6. MATLAB
6.1. Introduction to MATLAB
6.2. Programming
6.3. Averaging filter
6.4. Convolution
6.5. Fourier transform: DFT and FFT
6.6. Spatial filters
6.7. Frequency domain filters
6.8. Compression
6.9. JPEG and DCT
6.10. Audio
6.11. Wavelets
Teaching methods and general organization 

Official assessment of learning outcomes 
Examinationbased assessment

Reading and study resources 
Book
Bennett, C. ; Sharpley, R. Interpolation of operators. Boston [etc.] : Academic Press, 1988.
Duoandikoetxea, J. Fourier analysis. Providence, R.I. : American Mathematical Society, 2001.
Frazier, M. An introduction to wavelets through linear algebra. New York [etc.] : Springer, 1999.
Accés consorciat al llibre electronic
Grafakos, L. Classical fourier analysis. New York : Springer, 2014.
Guzmán, M. de. Real variable methods in Fourier analysis. Amsterdam [etc.] : NorthHolland, 1980.
Hernández, E. : Weiss, G. A first course on Wavelets. Boca Raton [Fla] [etc.] : CRC Press, 1996.
Walker, J. S. Fast Fourier transforms. Boca Raton [Fla.] [etc.] : CRC Press, 1996.