470-6103/01 – 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
YearSemesterwinter + summer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesUSP, FS, FEI, HGFIntended 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+0
Part-time Examination 28+0

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.

Additional study materials

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 • Passing an oral exam

E-learning

Other requirements

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

Full-time form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K English Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Optional study plan
2010/2011 (P2649) Electrical Engineering (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2017/2018 Summer