Double Degree in International Computer Engineering and Management of Business and Technology

Digital Signal Processing

Description
The subject of digital signal processing is an introduction to methods of processing digital signals in one dimension. In the course, students will learn how to process digital information with linear and time invariant systems from analog sources. Digital processing techniques, in both time and frequency domains, are explained. Also, the Z transform is introduced as an useful tool for filter design and analysis.
Type Subject
Optativa
Semester
First
Credits
4.00

Titular Professors

Previous Knowledge

Time and frequency characterization of analog signals and systems. Sampling Theorem.
Complex numbers and series of functions

Objectives
Contents

1 Characterization of discrete LTI systems. Impulse response
1.1 Introduction
1.2 The linear time invariant systems (LIT)
1.3 Impulse response and discrete linear convolution
1.4 Linear difference equations with constant coefficients

2 Fourier analysis for discrete signals and systems
2.1 Introduction to TFSD
2.2 Representation of frequency sequences by TFSD
2.3 Properties of TFSD
2.4 Digital processing of analog band limited signals
2.5 Changing the sampling frequency in the discrete domain (decimation and interpolation)

3 The Discrete Fourier Transform (D.F.T.)
3.1 Representation of periodic sequences: Discrete Fourier Series (DFS)
3.2 Properties of Discrete Fourier Series
3.3 The Fourier transform of periodic signals.
3.4 Sampling of TFSD
3.5 Frequency Representation of finite sequences. The Discrete Fourier Transform (D.F.T.)
3.6 Properties of D.F.T
3.7 Calculation of linear convolution using DFT
3.8 The fast Fourier transform (F.F.T.)

4 The Z transform
4.1 Introduction
4.2 Definition of Z transform
4.3 Properties of the region of convergence (ROC)
4.4 Properties of Z transform
4.5 The inverse transform Z
4.6 Study of linear and invariant systems with the transformed Z

Methodology

During the course, we combine different ways to teach the subject:

1. Tasks :

The students, grouped in teams, face the task proposed by the teacher. The duration of the tasks usually oscillates between 2 and 6 weeks , depending on their complexity. To carry out the task , the students have a documentation containing both an explanation of the theoretical concepts of the course as a description of how to apply these concepts in practice. The work culminates by conducting practical exercises that allow the student to dive deeply into the concepts and implement them in practice.

2. Sessions resolution of doubts

Approximately halfway of the execution of the task, the teacher organizes an open questions class session, during which he explains the concepts that students have not been able to grasp using the available documentation.

Evaluation

In order to assess whether the student has achieved an appropriate level of knowledge, the teacher has several means to obtain data from the student:

A. Exams .
For each task, validation tests of knowledge are performed, both individually and at group level. In addition, each task ends with the delivery of a deliverable, which is evaluated as if it were the result of an examination .

B. Orals .
The teacher will hold individual and group interviews to monitor the degree of achievement of the concepts developed for each task.

M. Data observed during group work .
The teacher has a list to record various observations made during the group work of students.

During the course students are informed of their individual and group marks that were obtained after each task.

Evaluation Criteria
Basic Bibliography

Documentation of the tasks
Procesado digital de la señal. Guía docente, Joan Claudi Socoró, José A. Morán y Germán Cobo, Ed, La Salle, 2009

Additional Material

T. K. Rawat, Signals and Systems, Oxford, 2010
A.V. Oppenheim i R. W. Schafer, Discrete Time Signal Processing, Prentice-Hall, 1999
Francesc Tarrés, Introducció al tractament digital del senyal, Bruño/EUETT, 1995