Signals and Systems

Credits
6
Types
Compulsory
Requirements
This subject has not requirements, but it has got previous capacities
Department
TSC
The set of techniques and algorithms that allow studying, detecting, transforming, processing, transmitting, and classifying signals is called signal processing. This course provides an introduction to the fundamental theory of this discipline for both one-dimensional and two-dimensional signals. During the course, signals and systems in the time and frequency domains are characterized by the Fourier transform in analog and discrete versions. The sampling theorem allows the processing of analog signals utilizing discrete techniques and applying computationally efficient algorithms. The course introduces the filter and filtering of signals, and filters are designed using specs in the frequency domain.

Teachers

Person in charge

  • Olga Muñoz Medina ( )

Others

  • Orestes Mas Casals ( )

Weekly hours

Theory
2
Problems
2
Laboratory
0
Guided learning
0
Autonomous learning
6

Competences

Technical Competences

Technical competencies

  • CE5 - Design and apply techniques of signal processing, choosing between different technological tools, including those of Artificial vision, speech recognition and multimedia data processing.

Transversal Competences

Transversals

  • CT5 [Avaluable] - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.

Basic

  • CB5 - That the students have developed those learning skills necessary to undertake later studies with a high degree of autonomy

Generic Technical Competences

Generic

  • CG1 - To design computer systems that integrate data of provenances and very diverse forms, create with them mathematical models, reason on these models and act accordingly, learning from experience.
  • CG2 - Choose and apply the most appropriate methods and techniques to a problem defined by data that represents a challenge for its volume, speed, variety or heterogeneity, including computer, mathematical, statistical and signal processing methods.
  • CG5 - To be able to draw on fundamental knowledge and sound work methodologies acquired during the studies to adapt to the new technological scenarios of the future.

Objectives

  1. The student must be able to understand and be proficient in the basic concepts of signals, linear systems, and related functions and transformations.
    Related competences: CG2, CG5, CB5,
  2. The student must know how to do the mathematical analysis of signals and systems in the time domain, for both analog and digital environments.
    Related competences: CG5, CB5,
  3. The student must know how to do the mathematical analysis of analog signals and systems in the frequency domain.
    Related competences: CG5, CB5,
  4. The student must know how to do the mathematical analysis of discrete-time signals and systems in the frequency domain.
    Related competences: CG5, CB5,
  5. The student must be able to evaluate discrete filters and apply them to real systems
    Related competences: CE5, CG2, CG5, CB5,
  6. The student must know how to correctly formulate a problem from the proposed statement and identify the options for its resolution, apply the appropriate resolution method, and validate the solution.
    Related competences: CT5, CG2, CB5,
  7. The student must know how to interpret and use discrete signals and systems in 1D and 2D in the temporal/spatial.
    Related competences: CE5, CG1, CG2,
  8. The student must be able to apply the frequency representation of signals and systems to solve various applications.
    Related competences: CE5, CT5, CG2,
  9. The student must know how to identify, model, and solve problems from open situations. Also, to explore and apply the alternatives for resolution. The student will work with approximations.
    Related competences: CE5, CG1, CG2, CG5,
  10. The student must know how to use autonomously the tools, instruments and software applications available in the laboratories of the basic and advanced subjects. He should know their performances and limitations.
    Related competences: CE5, CT5, CG1, CG2,
  11. The student should know additional tools useful for processing discrete generic signals in the time and transformed domains.
    Related competences: CE5, CG1, CG2,
  12. The student must be able to evaluate the advantages and disadvantages of different technological alternatives to implement analysis systems for analog and discrete signals.
    Related competences: CE5, CT5, CG2,

Contents

  1. Signals and systems in temporal (or spatial) domain
    Continuous-domain and discrete-domain signals and systems.
    Convolution.
    Correlation.
    Linear and time invariant systems.
  2. Continuous-Time signals and systems in the frequency domain
    Continuous-Time Fourier Transform (CTFT).
    Sampling and reconstruction.
  3. Discrete-Time signals and systems in the frequency domain
    Discrete-Time Fourier Transform (DTFT).
    Decimation and interpolation.
    Frequency analysis of discrete-time signals and systems.
    Discrete Fourier Transform (DFT).
  4. Representation, analysis and design of linear filters
    Z Transform.
    Linear filters design.

Activities

Activity Evaluation act


Analog and digital signals and systems

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 2 6
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Convolution

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 1 2 6
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Correlation

Attendance to lecture and problems session. Solving problems at home.
Objectives: 1 2 6
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Linear and Time-Invariant systems

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 1 2 6
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Continuous-Time Fourier Transform (CTFT)

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 6 3
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Sampling and reconstruction. Teorema de Nyquist

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 2 6 3
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Discrete-Time Fourier Transform (DTFT)

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 6 4
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Decimation and interpolation

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 2 6 4
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Frequency analysis of time-discrete signals and systems

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 6 4
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Discrete-Time Fourier Transform (DFT)

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 6 4
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Z Transform

- Definición de TZ, propiedades y ejemplos. - Caracterización de sistemas definidos mediante EDFs.
Objectives: 11 12
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Filters design

Attendance to lecture and problems session. Independent work on proposed problems.
Objectives: 8 5
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Lab: convolution and correlation

Lab.
Objectives: 7 9 5 10
Week: 4
Type: lab exam
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
2h

Lab: analysis of basic signals in the frequency domain

Lab.
Objectives: 8 10
Week: 9
Type: lab exam
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
2h

Lab: frequency analysis of speech signals

Lab.
Objectives: 8 10
Week: 11
Type: lab exam
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
2h

Lab: pre-processing of noisy ECGs

Lab.
Objectives: 8 5 10
Week: 14
Type: lab exam
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
2h

Mid-term exam


Objectives: 1 2 8 7 6 3
Week: 9
Type: theory exam
Theory
2h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
8h

Final exam


Objectives: 1 2 8 7 6 3 4
Week: 15 (Outside class hours)
Type: final exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
3h
Autonomous learning
16h

Test 1


Objectives: 2
Week: 5 (Outside class hours)
Type: theory exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
3h
Autonomous learning
0h

Test 2


Objectives: 3
Week: 7 (Outside class hours)
Type: theory exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
3h
Autonomous learning
0h

Test 3


Objectives: 4
Week: 12 (Outside class hours)
Type: theory exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
3h
Autonomous learning
0h

Teaching methodology

The course is based on face-to-face theory, problems and laboratory classes.

The theory classes follow the program defined in this teaching guide. Within the theory and problems classes, the dialogue between the teacher and the students is promoted, providing problems and joint activities based on particular aspects of the topic being discussed.

The laboratory classes focus on the topics of Fourier Transform, filtering and processing of signals. They are based on computer programs and are guided by a text.

Theory and problems classes will be in Spanish. Labs will be in Catalan.

Evaluation methodology

The final grade of the course is obtained from:

- Quizzes: Q (6%)
- The mid-term exam: P (19%)
- The final exam: F (60%)
- Lab: L (15%)


Final grade= max( 0.19 P + 0.06 Q + 0.15 L +0.6 F; 0.15 L + 0.85 F )

In the case of taking a Re-evaluation exam, the final grade is:

Final grade = 0.85 R+0.15 L

Bibliography

Basic:

Complementary:

Previous capacities

The knowledge acquired in the subjects of the Degree in the previous semester.