## APUNAP41 Fundamentals of Signal Analysis

Institute of physics in Opava
summer 2022
Extent and Intensity
1/3/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. Ing. Petr Čermák, Ph.D. (lecturer)
Guaranteed by
doc. Ing. Petr Čermák, Ph.D.
Institute of physics in Opava
Prerequisites
( FAKULTA ( FU ) && TYP_STUDIA ( B ))
None
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on digital processing of one-dimensional signals in physics, monitoring technology and other areas.
Learning outcomes
Upon completion of the course, the student will be able to: Describe and explain the term Continuous, discrete, digital signal, application areas, stages of signal processing, classification of discrete signal processing methods, advantages and disadvantages of discrete and digital signal processing, 1D, 2D signals, multidimensional.
describe and explain the Fourier series (FS) and the Fourier transform (FT) of a continuous signal. Definition and characteristics, FT of basic signals, describe and explain the Transmission function, impulse response of the system, distortion (binding to the transmission bandwidth).
describe and explain Digital filtration and construction of digital filters – FIR, IIR (numerical realization of convolutional integral, low-frequency filters for noise removal, narrowband filters, nonlinear filters, filters for removing shots).
Syllabus
• 1. Basic terms. Continuous, discrete, digital signal, application areas, stages of signal processing, classification of discrete methods of signal processing, advantages and disadvantages of discrete and digital signal processing, 1D, 2D signals, multidimensional.
• 2. Fourier series (FS) and Fourier transform (FT) of a continuous signal. Definition and properties, FT of basic signals, effect of sampling of the original on the image, convolution and correlation.
• 3. Signal sampling and reconstruction. Ideal and real sampling signal, sampling theorem and alias, reconstruction filter and interpolant.
• 4. Fourier transform of discrete signal. DTFT, DFT, their inversion and properties.
• 5. Discrete unitary transformations. Kernel transformations, unitarity, hermitism, examples: Hadamard, Walsh, DFT, Haar, methods of fast DFT calculation (FFT).
• 6. Deterministic and stochastic signals. Stability and causality, linear time invariant systems.
• 7. Transmission function, impulse response of the system, distortion (binding to transmission bandwidth).
• 8. Digital filtration and construction of digital filters – FIR, IIR (numerical realization of convolutional integral, low-frequency filters for noise removal, narrowband filters, nonlinear filters, filters for shot removal).
• 9. Wavelet transformations (WT). Time-frequency analysis, continuous, discrete WT (CWT/DWT), DWT tyou Daubechies, realization of WT by filter banks.
Literature
required literature
• Lyons R.G. Understanding Digital Signal Processing. Prentice Hall; 3 edition, 2010. ISBN 978-0137027415. info
recommended literature
• Jan, J.: Číslicová filtrace, analýza a restaurace signálů. Akademické nakladatelství, VUTIUM, 2002
Teaching methods
Forms of teaching will be as follows:
1. theoretical preparation (lectures);
2. laboratory exercises (processing of one dimensional signal).
Assessment methods
Active participation in exercises and solving all homework. Students demonstrate knowledge and overview of the area of signal analysis in the range of lectures on oral exam.
Language of instruction
Czech