E0440 Linear and Adaptive Data Analysis

Faculty of Science
Autumn 2022
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Ing. Daniel Schwarz, Ph.D. (lecturer)
Guaranteed by
doc. Ing. Daniel Schwarz, Ph.D.
RECETOX – Faculty of Science
Contact Person: doc. Ing. Daniel Schwarz, Ph.D.
Supplier department: RECETOX – Faculty of Science
Timetable
Tue 12:00–14:50 F01B1/709
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
There is a considerable increase in the amount of data, which represent processes, events and activities in living systems, together with the rapid developments in digital technology which allow us to acquire, transmit and store the data. Thus, there is also an increase in the importance of methods for digital signal processing and analysis. The goal of signal processing is to enhance signal components in noisy measurements or to transform measured data sets such that new features become visible. At the end of the course students should be able to understand and explain linear and adaptive techniques for signal processing and analysis. Students should be also able to design and use own linear system for denoising in the measured data and for suppression of distortion in the measured data.
Learning outcomes
After the course, students will be able to:
define basic terms and concepts: time series, signals, sequences, data;
reproduce and explain the sampling theorem;
calculate the signal-to-noise ratio (quantization noise) based on the number of A/D converter bits;
define a system;
explain the basic properties of LTI systems;
explain the principle of superposition;
program convolution operator;
analyze time series using the Fourier series;
analyze time series using unit pulses;
define impulse characteristics and frequency characteristics;
explain the principle of filtration;
list idealized filters and graphically express their frequency characteristics;
explain the relationship between DF, DTFT, FT and DFT;
explain the relationship between transfer function and frequency characteristic;
estimate the shape of the frequency response from the null and poles of the transfer function;
assess the stability of a LTI system;
categorize filters to FIR, IIR, AR, MA, ARMA;
design a FIR filter based on sampling frequency characteristics; apply filters to solve problems aimed at selecting harmonics of time series;
explain the terms normalized frequency and group delay;
define the term repetitive time series and list examples of repetitive time series from practice;
explain the principle of cumulation techniques;
identify conditions for the application of cumulation techniques;
program cumulation techniques with uniform weights and exponential weights;
graphically compare the dynamic properties of different cumulation techniques;
to distinguish between the additive and the multiplier model of the time series;
to distinguish a useful and non-systematic component of the time series;
divide a useful component of the time series into a trend and periodic component;
reformulate the seasonal and cyclical component into a general periodic;
remove the trend from the time series by interleaving and differentiating;
explain the principle of seasonal differentiation;
apply the exponential smoothing technique for predicting time series with prediction horizon 1;
list four models of stationary time series: AR, MA, ARMA and white noise;
explain the important properties of white noise;
construct a time series model based on autocorrelation function and partial autorocorelative function;
analyze the model's residual, thus validating the time series model;
assess the quality of model prediction;
apply all knowledge for ARIMA or SARIMA design for non-stationary time series;
describe the role of an optimal filter when identifying systems;
derive normal equations by minimizing the mean quadratic error;
design an optimal filter by algebraic solution of normal equations;
explain the concept of a whitening filter and describe the principle of inverse system identification;
explain the term adaptive filter;
program adaptive filter with LMS algorithm;
explain the difference between the mean quadratic error and the total quadratic error;
program adaptive filter with RLS algorithm;
apply adaptive filters to predict a non-stationary time series;
use the program to illustrate the weight convergence of the predictive adaptive filter;
Syllabus
  • P1: Signals, time series, data. Classification and properties of signals. Sampling theorem. Aliasing. Quantization.
  • P2: Systems: classification, examples, properties, superposition, causality, stability, LTI, convolution, impulse response - i.e. system description in time domain.
  • P3: Systems: frequency domain analysis, Fourier series, band-pass filters, Fourier transform, DTFT.
  • P4: Sampling and aliasing in detail.
  • P5: Linear filters, Z-transform, Stability.
  • P6: Linear filters, {AR, MA, ARMA} , {IIR, FIR}.
  • P7: Cumulative techniques, signal-to-noise ratio.
  • P8: Cumulative techniques.
  • P9: Random processes and time series models.
  • P10: Adaptive processing of data. Linear prediction, optimal filtering. LMS algorithm.
  • P11: Autoregressive processes and linear prediction - whitening filter. LMS filter variations.
  • P12: Adaptive filtering – RLS method.
  • P13: Time-frequency analysis with the use of wavelet transform. Nonlinear filtering for smoothing.
Literature
  • DEVASAHAYAM, Suresh R. Signals and systems in biomedical engineering : signal processing and physiological systems modeling. 1st ed. New York: Kluwer Academic/Plenum Publishers, 2000, xvi, 337. ISBN 0306463911. info
  • DRONGELEN, Wim van. Signal processing for neuroscientists : introduction to the analysis of physiological signals. Amsterdam: Academic Press, 2007, ix, 308. ISBN 9780123708670. info
  • Wavelets and their applications. Edited by Michel Misiti. London: ISTE, 2006, 330 s. ISBN 9781905209316. info
Teaching methods
lectures combined with practising on computers with the use of mathematical system Matlab
Assessment methods
oral examination through MS Teams
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://portal.matematickabiologie.cz/index.php?pg=analyza-a-modelovani-dynamickych-biologickych-dat--linearni-a-adaptivni-zpracovani-dat
The course is also listed under the following terms Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/E0440