The course introduces the basic mathematical concepts and tools for signal characterization and processing, which can be applied specifically to biomedical signals. Signals and systems are analyzed in continuous and discrete time, both in the time and frequency domain. Digital signal processing is introduced using sampling, DFT and multirate signal processing. A practical approach to the digital processing of biomedical signals is carried out using the MATLAB environment.



The course is part of the Fundamentals of Engineering module.



In this subject, knowledge taught in the following subjects is used:

- Calculus - Differential Equations and Numerical Methods

- Algebra - Computer Science - Statistics



The knowledge learned from this subject will be used in the following subjects:

- Advanced Biomedical Signal Processing - Control and Automation

- Biomedical Image Processing - Fundamentals of Electronics - Biomedical Equipment

- Biomedical Equipment

General skills:

G003 Knowledge in basic and technological subjects, which enable to learn new methods and theories, and provide versatility to adapt to new situations..



Transversal skills:

T001 Ability to solve problems with initiative, decision making, creativity and critical reasoning, respecting the principles of universal accessibility and design for all people..



Specific skills:

M02FI04 Knowledge, understanding and mastery of the basic concepts of linear systems, and their related functions and transforms in the field of biomedical engineering.



Learning outcome (degree):

RAG7 The graduate will be able to identify the concepts and techniques of the basic and technological subjects of engineering (drawing, computer science, electronics, electricity, mechanics, automation, communication technologies, energy) that enable him/her to learn new methods and theories and provide versatility to adapt to new situations.



RAT1 The graduate will be able to solve problems with initiative, decision-making, creativity and critical reasoning.

Topic 1. Introduction to biomedical signal processing.



Topic 2. Continuous and discrete signals in the time domain.

-Classification of signals. Basic signals. Transformation of the independent variable. Characterization of signals in the time domain.



Topic 3. Continuous and discrete systems in the time domain.

-Properties of systems. Linear time-invariant (LTI) systems. Convolution. Interconnection of LTI systems. LTI systemas described by means of differential equations and difference equations. Implementation of LTI systems.



Topic 4. Signal analysis in the frequency domain.

-Fourier series. Fourier transform. Properties.



Topic 5. Analysis of LTI systems in the frequency domain.

-Frequency response. Linear filtering. Types of filters. Discrete FIR and IIR filters.



Topic 6. Sampling.

-Sampling of continuous signals. AD and DA conversion.



Topic 7. Correlation and power spectrum.

-Auto-correlation and cross-correlation. Energy and power spectral density.



Topic 8. Discrete Fourier Transform (DFT).

-Definition. IDFT. Frequency sampling. Application using FFT algorithms.



Topic 9. Multirate digital signal processing.

-Interpolation and decimation. Applications.

The course is taught both individually and in groups. The masterclass part of the course is addressed individually, whereas the classroom exercises will combine both modalities, and the laboratory sessions are carried out in small groups.



The presentation of the necessary theoretical contents of the course, and the proposal and development of illustrative practical examples, as a whole, will serve to guide and stimulate the autonomous work of the students focused on solving new problems and questions that will be posed to them. Although individual work will come first, team work dynamics will be used to assess the work.



In the Lab Sessions, classroom time will be used for the development of basic signal processing applications using the MATLAB environment. Above all, the aim is to encourage teamwork through the proposal of practical tasks to be carried out collaboratively in the classroom. Classroom work will include writing a report for each practical task.



Non-classroom time associated to the theoretical content and problem solving should be used to revisit the basic concepts ant the theory presented in the classroom, as well as to work through the analytical and numerical problems - either individually or in groups. On the other hand, the non-classroom time associated to the lab sessions should be focused on both preparing the contents of th lab activities and completing/fine tuning their respective reports collaboratively. The teaching team will promote the completion of the bulk of the lab work within the classroom time.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 60
  • Realization of Practical Work (exercises, cases or problems) (%): 20
  • Team projects (problem solving, project design)) (%): 20

The theoretical/problem solving content (lecture-based + applied classroom-based groups) and the lab-based content are evaluated independently.

In order to pass the course, a minimum score of 5 points out of 10 must be obtained in each of the parts. Passing grades of any of the parts will be saved for the extraordinary exam.



Part 1. Evaluation of the theoretical/problem solving content (lecture-based + applied classroom-based groups). Total weight assigned: 75 %.



a) First mid-term exam: the first written midterm exam covers all topics from 1 to 4. It consists of short questions and problems. Weight assigned: 22 %. Minimum score required: 4 points out of 10.



b) On the official date of the ordinary call, two written exams will be held, in this order:

b.1) Second midterm exam: it covers topics 5 to 9, consisting of short questions and problems. Weight assigned: 38 %. Minimum score required: 5 points out of 10.

b.2) First midterm exam: recovery of topics 1 to 4 for those students that have not achieved the minimum score required in a). Weight assigned: 22 %. Minimum score required: 4 points out of 10. Taking this exam implies updating the previous score from a).



c) Delivery of solved problems at the end of each topic. Weight assigned: 15%. .



Part 2. Evaluation of laboratory sessions (applied laboratory-based groups). Total weight assigned: 25 %.



a) Reports. Assigned weight 20 %.

b) Presentation of the reports. Assigned weight 5 %.



In the event of failing any of the assessment mechanisms from above, the weighted formula will be applied to calculate the final score (GAUR score), being 4.5 points out of 10 the maximum possible score.



___________________________________________

Continuous assessment withdrawal



Students who decide to renounce the right to continuous assessment, they must request it formally (written request) to the teaching staff, within 9 weeks, starting from the beginning of the four-month period.



Students who opt fpr single assessment must take the two written exams as indicated in section b), items b.1 and b.2 (weight assigned: 75%). Additionally, they have to carry out a practical exam in the laboratory (weight assigned: 25%). In order to pass the course, a minimum score of 5 out of 10 must be obtained in each of the exams.



____________________________________________

Withdrawal from the ordinary call



Non-attendance at the exam call in the official date will result in a withdrawal (NOT PRESENTED will be applied).

In the extraordinary call, the theoretical/practical content (Part 1) and/or Lab session content (Part 2) will be assessed, depending on the part the student has pending to pass. Therefore, the partial scores obtained during the continuous assessment will not be considered in this call.



The evaluation of the theoretical/practical content (Part 1) will be carried out by means of a single written exam with questions and problems from all the topics of the course program (weight assigned: 75%).



The evaluation of the practical computer work (Part 2) will be carried out by means of a practical test in the laboratory (weight assigned: 25%).



In order to pass the course, a minimum score of 5 points out of 10 must be obtained in each of the tests. In the event of failing any of the assessment mechanisms from above, the weighted formula will be applied to calculate the final score (GAUR score), being 4.5 points (out of 10) the maximum possible score.

____________________________________________

Withdrawal of previous grades



Students who decide to renounce to their passing grades from Part 1 and/or Part 2 obtained in the ordinary call, they must request it formally (written request) to the teaching staff no later than ten days before the official date of the extraordinary call.



In this case, students must take the two tests on that date. In order to pass the course, students must obtain a minimum score of 5 points out of 10 in each of the tests. In the event of failing any of the assessment mechanisms from above, the weighted formula will be applied to calculate the final score (GAUR score), being 4.5 points (out of 10) the maximum possible score.

____________________________________________

Withdrawal from the extraordinary call



Non-attendance at the exam call in the official date will result in a withdrawal (NOT PRESENTED will be applied).

- Lecture notes, presentations and resources in the eGela virtual platform.
- Collections of basic and long problems in the eGela virtual platform.
- Materials for the laboratory computer work.

Basic bibliography

1. Oppenheim AV, Willsky AS. Signals and systems. Prentice Hall International, Inc. ISBN: 978-0138147570

2. Proakis JG, Manolakis DG. Introduction to Digital Signal Processing. Macmillan Publishing Company. ISBN 978-0023968105

3. Siebert WM. Circuits, Signals and Systems. Cambridge, MA; MIT Press, 1985. ISBN 978-02621192293.

4. Karu ZZ. Signals and Systems Made Ridiculously Simple. Huntsville, AL: ZiZi Press, 1995. ISBN 978-0964375215

In-depth bibliography

1. Bioelectrical signal Processing in cardiac and neurological applications. Elsevier Academic Press. ISBN 978-0124375529.
2. Semmlow JL. Biosignal and Biomedical image processing: Matlab-based applications. Marcel Dekker. ISBN 978-0824748036.