Ternopil Ivan Puluj National Technical University

Каф. біотехнічних систем

Biomedical Signal Processing


1. Educational programs for which discipline is mandatory:

# Educational stage Broad field Major Educational program Course(s) Semester(s)
1 16. Хімічна та біоінженерія 163. Біомедична інженерія (бакалавр) Біомедична інженерія 3 6

2. The course is offered as elective for all levels of higher education and all educational programs.

3. Information about the author of the course

Full name Шадріна Галина Михайлівна
Academic degree Cand. Sc.
Academic title Assoc. Prof.
Link to the teacher`s page on the official website of the University http://library.tntu.edu.ua/personaliji/a/sh/shadrina-halyna-myhajlivna/
Е-mail (in the domain tntu.edu.ua) shadrina@tntu.edu.ua

4. Information about the course

Study hours structure Lectures: 36
Practical classes: 36
Laboratory classes: 36

Amount of hours for individual work: 102
ECTS credits: 7
Teaching language english
Form of final examination exam
Link to an electronic course on the e-learning platform of the university https://dl.tntu.edu.ua/bounce.php?course=5540

5. Program of discipline

Description of academic discipline, its goals, subject of study and learning outcomes

The purpose of the study of the discipline: acquisition of knowledge by biomedical signal processing methods and methods of their implementation in the form of algorithms and computer programs.
Tasks of the discipline: application of physical and biophysical methods of investigation of the state of biological objects, diagnostics of the state and management of it with the use of energy, real and informational influences.

The place of academic discipline in the structural and logical scheme of study according to the educational program

Prerequisites. List of disciplines, or knowledge and skills, possession of which students needed (training requirements) for successful discipline assimilation

Biomedical Processes and Signal Modeling

List of disciplines based on learning results from this discipline

Fundamentals of biomechanics
Fundamentals of Interaction of Physical Fields with Bioobjects

Contents of the academic discipline

Lectures (titles/topics)

Topic 1. Biomedical signals, their classification, the main provisions for their receipt and processing. Biomedical signals. Types of biosignals. Basic methods of studying the functional state of the human body. The task of receiving and analyzing biosignals.
Topic 2. Biomedical signals, noise and their mathematical description for the problem of processing. Biomedical signal-model-method-algorithm-program. Mathematical description of biosignals. Stochastic biosignals.
Topic 3. Digital biomedicalsignal processing. How to implement digital processing for biosignals. Advantages of digital signal processing.
Topic 4. Correlation analysis of biomedical signals. Energy characteristics of biomedical signals. Offset (shift) of signals in time. Correlation characteristics of biomedical signals. Pearson correlation coefficient.
Topic 5. Fourier analysis. Why we need signal transformation. Properties of Fourier transform. Fast Fourier transform and its advantage. Harmonic analysis of biomedical signals. Geometric data model. The distance between the signals. Representation of biomedical signals in the form of sum of series of elementary functions. Harmonious analysis of periodic biomedical signals. Properties of the Fourier series.
Topic 6. Spectra of periodic biomedical signals. Energy characteristics of periodic biomedical signals. Basic principles of the theory of spectra, operations on spectra. The relationship between effective spectrum width and signal duration. Spectrum of nonperiodic biomedical signals. Reference theorem. Representation of Biomedical Signals by Laplace Transformation. Link with the Fourier and Laplace transforms.
Topic 7. Spectral correlation analysis of random biomedical signals. Connection of the covariance function of a random signal with its energy spectrum, Wiener-Khinchin theorem. Mutual correlation function and mutual spectral density of two random processes.
Topic 8. Statistical analysis of random biomedical signals. Physical nature of random biomedical signals. Covariance function of random biomedical signal. Stationary and agility. Interconnection of the basic characteristics of random signals. Statistical methods for the analysis of random biomedical signals.
Topic 9. Random signal with normal probability density distribution law (Gaussian process). Two-dimensional probability density and energy spectrum of random process.
Topic 10. Wavelet treatment of biomedical signals. basic functions, basic properties, the principle of multiple-scale data analysis.
Topic 11. Periodically correlated random process as a model of biomedical signals. Properties of biomedical signals. Power theory of stochastic random processes. PCI as a model of biosignals.
Topic 12. Synthesis method of biomedical signals processing. The essence of the method. The algorithm of the common-mode processing method.
Topic 13. Component method for processing biomedical signals. The essence of the method. The algorithm of the component method of processing.
Topic 14. A filter method for biomedical signals processing. The essence of the method. Algorithm of a filter processing method.
Topic 15. Non-recursive digital filters. Types of filters. Method for calculating non recursive digital filters. Filters with linear phase characteristics. Ideal frequency filters. Final approximation of ideal filters. Smooth frequency digital filters. Differentiating digital filters. Alternative methods of calculating non-recursive digital filters.
Topic 16. Z-transformations of signals. Definition of Z-transform. Z-transformation mapping. Z-polynomial space. Properties of Z-transformation. Reverse Z-transformation. Application of Z-transformation.
Topic 17. Recursive digital filters. The principle of recursive filtration. Development of recursive digital filters. Bilinear Z-transformation. Types of recursive frequency filters. Butterworth low-pass filter. Butterworth's high-frequency filter.
Topic 18. Discrete convolution. Discrete convolution (convolution). Discrete convolution equation. Technique of convolution.

Practical classes (topics)

1. Correlation processing of biosignals
2. Spectral processing of biosignals (DFT, FFT)
3. Laplace transform
4. Z-transform
5. Spectral correlation processing of biosignals
6. Statistical processing of biosignals
7. Wavelet processing of biosignals
8. Single-phase processing
9. Component method for processing biosignals

Laboratory classes (topics)

1. Introduction to MATLAB possibilities for signal processing.
2. Operators MATLAB for control the computing process.
3. Operation with vectors and matrices. Time vectors and sinusoids. Wave form generation.
4. Discrete Fourier transform. Fast Fourier transform.
5. Z-transform.
6. SPTool – an Interactive Signal Processing Environment.
7. Filter design.
8. Operations with functions.
9. Wavelet Toolbox using for biosignals wavelet analysis.
10. Graphic design of the results of processing biomedical signals in the form of 2D-graphs.
11. Graphic design of biomedical signal processing results in the form of 3D graphs.
12. Load biosignals and save processing results to a file.

Individual work of a student / postgraduate student

Self study

Name of work Number of hours

1. Working out of separate sections of the program that are not presented at the lecture: 57 –
Topic 1. Measuring transducers of biomedical signals 5 –
Topic 2. Correlation of the additive mixture of biomedical signals and interferences. 5 –
Topic 3. Nonparametric methods of spectral evaluation of biomedical signals. 5 –
Topic 4. Regression analysis. 5 –
Topic 5. Algorithm for recovering the sampled biosignal. Recovery errors 5 –
Topic 6. Fast Fourier Transform Algorithms for an arbitrary composite biomedical signal 5 –
Topic 7. Estimation and accuracy of non-recursive digital filters. 5 –
Topic 8. Analytical form of Z-transformation 5 –
Topic 9. Estimation and accuracy of recursive and non-recursive digital filters. 5 –
Topic 10. The filter method of processing biomedical signals 4 –
Topic 11. Z-transformations of signals 4 –
Topic 12. Discrete convolution 4 –
3. Performance of course papers 30 –
4. Preparation for laboratory and practical classes 30 –
5. Preparation and exam preparation, testing 3 –
TOTAL hours: 120 –

Learning materials and resources

1. Abakumov VG, Gotra ZY, Zlepko SM Registration, processing and control of biomedical signals, Vinnytsia, 2011. 352 p.
2. Abakumov VG, Geranin VO, Rybin OI, Svatosh J., Sinekop YS Biomedical signals and their processing. Kyiv, 1997. 352 p.
3. Rangayan RM Analysis of biomedical signals. Practical hike. Per. with English under ed. A.P. Restless. Moscow, 2007. 440 p.
4. Babak VP, Handetsky VS, Shrufer E. Signal processing: A textbook for students of technical specialties. Kyiv, 1996.
5. Shrufer E. Signal processing: digital processing of sampled signals: Textbook for students of technical specialties of universities. Kiev, 1995.
6. Sergienko A.B. Digital signal processing. St. Petersburg, 2003. 604 p.

6. Policies and assessment process of the academic discipline

Policies of the discipline

The policy of the subject is determined by the system of requirements that the teacher makes to the student when studying the discipline " Biomedical signal processing " and is based on the principles of academic virtue.
Requirements relate to attending classes (inadmissibility of absences, delays, etc.); rules of conduct in the classroom (active participation, fulfillment of the required minimum of educational work, etc.) motivation and penalties (for which points can be awarded or deducted, etc.).
The policy of the academic discipline " Biomedical signal processing " is built taking into account the norms of Ukrainian legislation regarding academic virtue, the Statute, the provisions of TNTU:
1 Regulations on the organization of the educational process at the Ternopil National Technical University named after Ivan Pulyui - order No. 4 / 7-340 of 05/21/2015 as amended on 06/25/2019 - order No. 4 / 7-622 of 06/27/2019 and of 04/14/2020 - order No. 4 / 7-243 dated 04/15/2020
2 Regulations on the individual curriculum of a student of Ternopil National Technical University named after Ivan Pulyuy (new edition) - order No. 4 / 7-669 of 09/25/2020
3 Regulations on academic mobility of participants in the educational process of Ternopil National Technical University named after Ivan Pulyuy
4 Regulations on the assessment of applicants for higher education of the Ternopil National Technical University named after Ivan Pulyuy (new edition) - order No. 4 / 7-670 of 09/25/2020
5 Provisions on academic mobility of students of TNTU named after I. Puluy - order No. 4 / 7-454 of 16.07.2013
6 Regulations on the settlement of conflict situations in the Ternopil National Technical University named after Ivan Pulyuy - order No. 4 / 7-164 of 03/01/2021
7 Regulations on the final semester control of the learning outcomes of students of the Ternopil National Technical University named after Ivan Pulyuy - order No. 4 / 7-122 of February 17, 2020
8 Temporary procedure for semester control and certification of applicants for higher education of Ternopil National Technical University named after Ivan Pulyuy - order No. 4 / 7-350 of 05/25/2020
Regulations on the prevention of academic plagiarism at the Ternopil National Technical University named after Ivan Pulyuy - order No. 4 / 7-964 dated 01.11.2019 as amended on 19.12.2019 order No. 4 / 7-114 dated 12.02.2020, as amended on 26.01.2021 - order No. 4 / 7-72 dated 02.02.2021
Regulations on the academic virtue of the participants in the educational process of the Ternopil National Technical University named after Ivan Pulyuy - order No. 4 / 7-969 dated 01.11.2019
Charter of Ternopil National Technical University. I. Pulyuya (new edition) - order of the Ministry of Education and Science No. 248 of February 25, 2019

Assessment methods and rating system of learning results assessment

Criteria of students’ progress assessment
Module 1 – 40 points:
10 points – test,
30 points – lab and practical works.
Module 2 – 35 points:
10 points – test,
25 points – lab and oractical works.
Form of final control – examination – max 25 points

Table of assessment scores:

Assessment scale
(100 points)
(4 points)
90-100 Excellent А
82-89 Good B
75-81 C
67-74 Fair D
60-66 E
35-59 Poor FX
1-34 F

7. Additional Information

Fourier transform
Autoregressive (AR)
Modified covariance
Subspace-based methods
Time-frequency analysis
Short time Fourier transform (STFT)
Wigner-Ville distribution
Choi-Williams distribution
Wavelet analysis
Continuous wavelet transform (CWT)
Discrete wavelet transform (DWT)
Wavelet packet decomposition (WPD)
Tunable Q-wavelet transform (TQWT)
Dual tree complex wavelet transform (DTCWT)
Empirical mode decomposition (EMD)
Ensemble empirical mode decomposition (EEMD)
Complete ensemble empirical mode decomposition (CEEMD)
Approved by the department
Biotechnical systems
(protocol №
on «