Spectra and harmonic analysis
| Title | Φασματική και αρμονική ανάλυση / Spectra and harmonic analysis |
| Code | 03YG014 |
| Faculty | Engineering |
| School | Rural and Surveying Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Vergos |
| Common | No |
| Status | Active |
| Course ID | 600025726 |
Programme of Study: PPS Tmīmatos Agronómōn kai Topográfōn Mīchanikṓn (2025-sīmera)
Registered students: 59
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core Courses | Core Courses | 3 | 2 | 5 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600267786
|
Course Type 2021
General Foundation
Course Type 2016-2020
- Background
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600267786
- eLearning: https://elearning.auth.gr/course/view.php?id=254
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
The course has no special prerequisites for attendance. However, good knowledge of mathematics (01YG005) and statistics (02YG010) is recommended.
Learning Outcomes
Introduction to spectral analysis of continuous and discrete signals as well as Fourier series. Connection of spectral methods with the data and practices of Rural and Surveying Engineering and their applications. Development of specialized algorithms in Matlab for the estimation of Fourier transforms, the spectral analysis of data and the application of digital filters.
• Understands Fourier series and Fourier transforms at a satisfactory level
• Analyzes their usefulness in topics related to the science of Topographic Engineering
• Develops signal processing methodologies in the frequency domain
• Estimates and infers signals from their spectral analysis and energy
• Uses spectral methods in signal analysis
• Computes series and Fourier transforms and builds code for it
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Be critical and self-critical
Course Content (Syllabus)
Fourier series in the plane and sphere. Direct and inverse Fourier transform in one and more dimensions. Fundamentals, properties and theorems of Fourier analysis. Power and energy signals, linear systems and filters. Discrete Fourier transforms and their numerical computations. Hanker and Hartley transforms. Introduction to wavelets. Application of Fourier analysis to Geoinformatics.
Keywords
signal processing, spectral analysis, Fourier analysis, convolution, FFT, wavelets, linear systems, filters
Educational Material Types
- Notes
- Slide presentations
- Multimedia
- Interactive excersises
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Laboratory Teaching
- Use of ICT in Communication with Students
Description
Information Technologies are used in the course teaching (educational material, video, presentations, etc), in laboratory exercises and in the communication of teachers with the students.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | ✓ | ||
| Laboratory Work | 20 | ✓ | ✓ | ||
| Reading Assigment | 20 | ✓ | |||
| Project | 23 | ✓ | |||
| Written assigments | 20 | ✓ | |||
| Exams | 3 | ||||
| Total | 125 |
Student Assessment
Description
Midterm exam, final exam, term project in Matlab and take-home exercises.
Students are evaluated by:
80% Written exams with theory questions and problem solving
20% Individual semester work on exercises and term project in Matlab.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
1. Λιάβας, Α., & Καρυστινός, Γ.(2024). Σήματα και Συστήματα [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. http://dx.doi.org/10.57713/kallipos-1051
2. Ανάλυση Fourier, Μurray R. Spiegel. Κωδικός Βιβλίου στον Εύδοξο: 2517
3. Διδακτικές σημειώσεις σε έντυπη και ηλεκτρονική μορφή, Α. Δερμάνης, Η.Ν. Τζιαβός
Additional bibliography for study
Ξενόγλωσση
Davis J.C. (1973): Statistics and Data Analysis in Geology. John Wiley & Sons.
Dermanis A. and L. Biagi (2002): Telerilevamento. Casa Editrice Ambrosiana. Milano.
Hsu H.P. (1984): Applied Fourier Analysis. Harcourτ Brace College Outline Series.
Ingle V.K and J.G. Proakis (2000): Digital Signal Processing Using MATLAB. Brooks/Cole, BookWare Companion Series.
Kamen E.W. and B.S. Heck (2000): Fundamentals of Signals and Systems Using the WEB and MATLAB. Pentice Hall.
Oppenheim A.V. and R.W. Schafer (1989): Discrete-Time Signal Processing. Pentice Hall.
Sideris M.G. (1984): Computation of Gravimetric Terrain Corrections Using Fast Fourier Transform. M.Sc. Thesis, UCSE Report #20007, University of Calgary.
Spiegel M.R. (1978): Ανάλυση Fourier (μτφ. Σ.Κ. Περσίδης). Schaum’s Outline Series, McGraw Hill, New York, ΕΣΠΙ, Αθήνα.
Stephenson G. (1974): Μαθηματικαί Μέθοδοι (μτφ. Θ. Κακούλλου και Β. Καλομοίρη). Τεύχος 2, Αθήνα.
Tolstov G.P. (1976): Fourier Series (translated from the Russian by R.A. Silverman). Dover publications, Inc., New York.
Tziavos I.N. (1992): Numerical Considerations of FFT Methods in Gravity Field Modeling. Wiss. Arb. d. Fachr. Vermwesen, Univ. Hannover, Nr. 188, Hannover.
Ελληνική
Δερμάνης Α. (1999): Διαστημική Γεωδαισία και Γεωδυναμική – GPS. Εκδόσεις Ζήτη, Θεσσαλονίκη.
Δερμάνης Α. και Η.Ν. Τζιαβός (2007): Σήματα και φασματικές μέθοδοι στη Γεωπληροφορική. Διδακτικές σημειώσεις, Θεσσαλονίκη.
Κατσάμπαλος Κ. (1987): Εφαρμογές Μαθηματικών σε Προβλήματα Αγρονόμου Τοπογράφου Μηχανικού. Διδακτικές σημειώσεις, Θεσσαλονίκη.
Κατσάμπαλος Κ. και Η.Ν. Τζιαβός (1992): Φυσική Γεωδαισία. Εκδόσεις Ζήτη, Θεσσαλονίκη.
Μερτίκας Σ. (1999): Τηλεπισκόπηση και Ψηφιακή Ανάλυση Εικόνας. Εκδόσεις ΙΩΝ, Αθήνα.
Μπίτης Γ.Α. (1973): Ασκήσεις Ανωτέρων Μαθηματικών. Θεσσαλονίκη.
Πανάς Σ.Μ. (1992): Επεξεργασία Αναλογικών Σημάτων. University Press Studio, Θεσσαλονίκη.
Πήτας Ι. (1996): Ψηφιακή επεξεργασία εικόνας. ΑΠΘ.
Ρετζεπέρης Π.Ι. (1980): Εισαγωγή στην Ανάλυση Fourier με Εφαρμογές στη Φυσική. Θεσσαλονίκη.
Τζιαβός H.N. (1997): Στοχαστικές Μέθοδοι στις Γεωεπιστήμες – Συστήματα εισόδου/εξόδου. Σημειώσεις για το μεταπτυχιακό πρόγραμμα σπουδών του ΤΑΤΜ/ΑΠΘ.
Τζιαβός H.N. (1999): Αριθμητική ανάλυση – Διακριτός και ταχύς μετασχηματισμός Fourier σε μία και δύο διαστάσεις. Σημειώσεις για το μεταπτυχιακό πρόγραμμα σπουδών του ΤΑΤΜ/ΑΠΘ.
Χρήσιμοι δικτυακοί τόποι
http://www.mathworks.com/ (Επίσημη ιστοσελίδα Matlab)
http://www.mathtools.net/ (Οδηγοί, προγράμματα, εργαλειοθήκες και οδηγίες για το πρόγραμμα Matlab)
http://www.cs.ubc.ca/~murphyk/Bayes/software.html
http://www.falstad.com/fourier/
http://www.sosmath.com/fourier/fourier1/fourier1.html
http://en.wikibooks.org/wiki/Signals_and_Systems/Fourier_Series
http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-003Fall-2003/LectureNotes/
http://dualist.stanford.edu/~ee265/handout.html
http://www.jhu.edu/~signals/lecture1/frames.html
http://www.mathworks.com
http://en.wikipedia.org/wiki/Fourier_transform
http://www.fftw.org/
Last Update
20-05-2025
