Ternopil Ivan Puluj National Technical University
Каф. біотехнічних систем
Biomedical Signal Processing
syllabus
1. Educational programs for which discipline is mandatory:
#  Educational stage  Broad field  Major  Educational program  Course(s)  Semester(s) 

1  bachelor's  16. Хімічна та біоінженерія  163. Біомедична інженерія (бакалавр)  3  6 
2. The course is offered as elective for all levels of higher education and all educational programs.
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 elearning 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.
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
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 signalmodelmethodalgorithmprogram. 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, WienerKhinchin 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). Twodimensional probability density and energy spectrum of random process.
Topic 10. Wavelet treatment of biomedical signals. basic functions, basic properties, the principle of multiplescale 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 commonmode 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. Nonrecursive 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 nonrecursive digital filters.
Topic 16. Ztransformations of signals. Definition of Ztransform. Ztransformation mapping. Zpolynomial space. Properties of Ztransformation. Reverse Ztransformation. Application of Ztransformation.
Topic 17. Recursive digital filters. The principle of recursive filtration. Development of recursive digital filters. Bilinear Ztransformation. Types of recursive frequency filters. Butterworth lowpass filter. Butterworth's highfrequency filter.
Topic 18. Discrete convolution. Discrete convolution (convolution). Discrete convolution equation. Technique of convolution.
Topic 2. Biomedical signals, noise and their mathematical description for the problem of processing. Biomedical signalmodelmethodalgorithmprogram. 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, WienerKhinchin 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). Twodimensional probability density and energy spectrum of random process.
Topic 10. Wavelet treatment of biomedical signals. basic functions, basic properties, the principle of multiplescale 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 commonmode 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. Nonrecursive 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 nonrecursive digital filters.
Topic 16. Ztransformations of signals. Definition of Ztransform. Ztransformation mapping. Zpolynomial space. Properties of Ztransformation. Reverse Ztransformation. Application of Ztransformation.
Topic 17. Recursive digital filters. The principle of recursive filtration. Development of recursive digital filters. Bilinear Ztransformation. Types of recursive frequency filters. Butterworth lowpass filter. Butterworth's highfrequency 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. Ztransform
5. Spectral correlation processing of biosignals
6. Statistical processing of biosignals
7. Wavelet processing of biosignals
8. Singlephase processing
9. Component method for processing biosignals
2. Spectral processing of biosignals (DFT, FFT)
3. Laplace transform
4. Ztransform
5. Spectral correlation processing of biosignals
6. Statistical processing of biosignals
7. Wavelet processing of biosignals
8. Singlephase 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. Ztransform.
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 2Dgraphs.
11. Graphic design of biomedical signal processing results in the form of 3D graphs.
12. Load biosignals and save processing results to a file.
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. Ztransform.
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 2Dgraphs.
11. Graphic design of biomedical signal processing results in the form of 3D graphs.
12. Load biosignals and save processing results to a file.
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.
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
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
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  
VNZ (100 points) 
National (4 points) 
ECTS 
90100  Excellent  А 
8289  Good  B 
7581  C  
6774  Fair  D 
6066  E  
3559  Poor  FX 
134  F 
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