UFPF009 Analysis and digital signal processing

Faculty of Philosophy and Science in Opava
Winter 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Stanislav Hledík, Ph.D. (lecturer)
Mgr. Adam Hofer (seminar tutor)
Guaranteed by
doc. RNDr. Stanislav Hledík, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
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 focuses on digital processing and analysis of one-dimensional signals in the natural sciences, especially in physics and in measuring and monitoring technology. The lectures are supplemented by practical demonstrations and interactive demonstrations.
Syllabus
  • Introduction. Basic concepts, systems and signals in continuous and discrete time. Properties and classification of discrete and digital signal processing, time and amplitude discretization, stage of processing and application areas.
    Discrete Signals and Systems. Sampling and reconstruction, the sampling theorem. Z -transform, discrete linear systems.
    Discrete linear transformations. Development of periodic functions in the harmonic series, Fourier series and their properties. The continuous Fourier transform and its properties. General discrete unitary transformation, discrete Fourier transform ( DFT) and its fast calculation method (FFT ). Cosine and sine transformation. Convolution and deconvolution, correlation and autocorrelation using DFT. Wavelet transform continuous and discrete filter banks.
    Random signals and processes. Correlation and covariance functions, stationary and ergodic processes, spectra, and relative power spectrum. Transmission of random signal linear system.
    Spectral analysis. Spectral analysis of deterministic, periodic, and general stochastic signals. Time-frequency analysis. Estimation of power spectra. Mutual spectrum.
    Correlation analysis. Properties of correlation, covariance, autocorrelation and autocovariance functions. Methods of estimating correlation functions. Correlation analysis of the signal.
    Linear signal filtering. Principles of digital filtering. FIR and IIR filters. Convolution, convolution theorem, filtering in the frequency domain. Types of filters.
    Nonlinear and adaptive signal filtering. Nonlinear discrete dynamical systems, general and polynomial nonlinear discrete systems, filters based on sorting, filtering homomorfická. Power cepstrum. Nonlinear matched filters. Adaptive filters, the types and applications, a linear adaptive prediction, adaptive interference suppression.
    Restaurant signal. Model bias, and the pseudoinverse deconvolution. Wiener filtering, Kalman filtering. Anti-aliasing ( smoothing ) of data. Deconvolution to optimize the shape of the impulse response. The method of entropy maximization.
    Detection of small signals in noise. The correlation properties of the useful signal and noise. Finding known phenomena in which the signal is correlated. Correlation and autocorrelation method, its use ( Radar, reflectometry), practical methods of calculating the autocorrelation function.
    Signal compression. Lossless compression, medium level of information, entropy, predictive coding, delta - coding, entropy coding, basic computer lossless compression formats. Lossy compression, redundant components, properties recipient signal components from the transformed signal subband coding, masking, basic computer lossy compression formats.
Literature
    recommended literature
  • Lyons R.G. Understanding Digital Signal Processing. Prentice Hall; 3 edition, 2010. ISBN 978-0137027415. info
  • Oppenheim A.V., Schafer R.W. Discrete-Time Signal Processing. Prentice Hall; 3 edition, 2009. ISBN 978-0131988422. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attendance at lectures is recommended. It can be substituted by the self-study of recommended literature and individual consultations. Tutorial attendance is compulsory (min. 80%).
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2022.
  • Enrolment Statistics (Winter 2021, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2021/UFPF009