Time and frequency characterization of analog signals and systems. Sampling Theorem.
Complex numbers and series of functions
1 Characterization of discrete LTI systems. Impulse response
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
4.2 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
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.
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.
Documentation of the tasks
Procesado digital de la señal. Guía docente, Joan Claudi Socoró, José A. Morán y Germán Cobo, Ed, La Salle, 2009
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