General information |
Course unit name: Applied Harmonic Analysis
Course unit code: 568183
Academic year: 2018-2019
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 |
Face-to-face learning activities |
60 |
- Lecture |
30 |
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- Lecture with practical component |
15 |
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- Laboratory session |
15 |
Supervised project |
20 |
Independent learning |
70 |
Recommendations |
Further recommendations
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Competences to be gained during study |
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Learning objectives |
Referring to knowledge
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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 |
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Official assessment of learning outcomes |
Examination-based assessment
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Reading and study resources |
Consulteu la disponibilitat a CERCABIB
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.] : North-Holland, 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.