Information System of Masaryk University 

Course Information

M7120 Spectral Analysis I

Faculty of Science
autumn 2011

Extent and Intensity

2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Teacher(s)

Mgr. Jiří Zelinka, Dr. (lecturer)

Supervisor

prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science

Timetable

Mon 10:00–11:50 M3,01023

Prerequisites

M4170 Measure and Integral && M6150 Functional Analysis I
Calculus of complex numbers, Differential calculus and Lebesgue integral, Linear functional analysis

Course Enrollment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

Fields of study the course is directly associated with

• Mathematics (programme PřF, M-MA)
• Mathematics (programme PřF, N-MA)

Course objectives

The course is an introduction to the Fourier spectral analysis of both periodic and nonperiodic functions.
After completing the course, students will be able to use methods of Fourier analysis to solve various problems, eg when solving differential equations.

Syllabus

• Fourier series (FS): 3 equivalent forms of FS (complex, trigonometric and amplitude-phase form), Dirichlet kernel and pointwise convergence, Fejér kernel and convergence in mean, convergence in spaces $L^1$ and $L^2$, statements on cyclic convolution and correlation, Parseval identities.
• Fourier transform (FT): existence and inversion (theorems by Fourier and Plancherel), properties, statements on convolution and correlation, Parseval identities, examples.
• Multivariate Fourier series and transforms.

Literature

• HOWELL, Kenneth B. Principles of Fourier Analysis (Principles of Fourier Analysis). Boca Raton-London-New York-Washington: Chapman & Hall, 2001. 776 pp. Studies in Advanced Mathematics. ISBN 0-8493-8275-0. info
• BRACEWELL, Ronald Newbold. Fourier transform and its applications. 2nd ed. New York: McGraw-Hill, 1986. xx, 474 s. ISBN 0-07-007015-6. info
• BRIGHAM, E. Oran. Fast Fourier transform. Englewood Cliffs: Prentice Hall, 1974. 252 s. ISBN 0-13-307496-. info
• KUFNER, Alois and Jan KADLEC. Fourierovy řady (Fourier series). Praha: Academia, 1969. info
• LASSER, Rupert. Introduction to fourier series. New York: Marcel Dekker, 1996. vii, 285 s. ISBN 0-8247-9610-1. info
• HARDY, G. H. and W. W. ROGOSINSKI. Fourierovy řady : Fourier series (Orig.). Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1971. 155 s. info

Teaching methods

Teaching is through lectures.

Assessment methods

Oral exam.

Follow-Up Courses

• M0120 Wavelet Analysis
• M8120 Spectral Analysis II

Further comments (probably available only v češtině)

Study Materials
The course is taught annually.

Listed among pre-requisites of other courses

• M8120 Spectral Analysis II
  M7120  

Teacher's information

http://www.math.muni.cz/~mkolar
Aktuální informace pro daný akademický rok a soubory ke stažení lze nalézt na webové stránce předmětu.

The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, autumn 2012, autumn 2013.

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• Enrollment Statistics (autumn 2011, recent)
  
• Permalink: https://is.muni.cz/course/sci/autumn2011/M7120

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