470-6103/02 – Applets of Integral and Discrete Transforms (VSIDT)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Ing. David Horák, Ph.D.Subject version guarantordoc. Ing. David Horák, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEI, HGF, FSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+14
Combined Examination 28+14

Subject aims expressed by acquired skills and competences

Student should be able to apply gained theoretical knowledges to solve particular engineering problem and defend chosen solution approach.

Teaching methods

Lectures
Project work

Summary

Lectures contain general view of the theory of integral transforms based on functional analysis and generalized functions. They contain both continuous and discrete integral transforms, their applications to engineering problems using mathematical software.

Compulsory literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994. William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0.

Recommended literature:

Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1.

Way of continuous check of knowledge in the course of semester

Requirements for passing the subject: • Submitting and successful defense of an individual project dealing with implementation and application of discrete transforms - max 40 points. • Passing an oral exam - max 60 points.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Introduction to integral transforms. Linear spaces, norm, scalar product. Hilbert space. Convergence of series and integrals. Orthogonal systems, series and function convolutions. Laplace and Fourier transforms. Inverse transforms. Fourier-Laplace transform. Discrete transforms. Discrete L-transform (Dirichlet series). Discrete Fourier transform. Discretization errors. FFT algorithm. Distribution, Dirac's impuls, L-image, F-image of distribution. Distribution reprezentation. Convolution as a general integral transform. Inverse convolution. Decomposition. Window function. Introduction to harmonic analysis. Shanonn-Kotelnik theorem. Mathematical filters, Gabor's transform. Window Fourier transform. Regularization. Generalized Fourier series and wavelets (time-frequency analysis). Wavelet bases, properties, construction. Continuous wavelet transform. Discrete wavelet transform. Multiresolution decomposition (MRA). Pyramid's algorithm. Packet decomposition. Data compression, signal reconstruction and other applications. Software for discrete transforms.

Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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