Systems and Signals

Objectives

The course introduces the elementary theoretical and practical basis of discrete-time and continuous time Signals and Systems. Particular emphasis is on the frequency representations common in signal processing applications, the continous-to-discrete time conversion, and the analysis of linear and invariant dynamical systems

Program

1. Signal concepts

1.1 continuous and discrete signals

1.2 Transformations of the independent variable

1.3 Exponentials and sinusoidals

1.4 Unit impulse and unit step

2. Systems Concepts

2.2 continuous and discrete time

2.3 Basic properties of systems: memory, causality, invariance, linearity, stability, inversibility

3. Linear and time invariant system (SLIT)

3.1 Discrete SLIT: Discrete Convolution

3.2 Continuous SLIT: continuous convolution

3.3 Properties of SLITs

3.4 Causal SLITs described by differential equations and difference equations

4. Fourier Series (FS)

4.1 FS of continuous time signals

4.2 Exponentials as proper functions of SLITs

4.3 Representation of periodic signals in FS

5. Fourier Transform (FT)

5.1 Fourier transform of continuous and discrete signals

5.2 Representation of aperiodic signals via FT

5.3 Frequency response, filtering

6. FT of discrete signals

6.1 Spectrum of discrete-time signals

6.2 SLITs described by difference equations

7. Sampling

7.1 Discrete-time processing of continuous-time signals

7.2 Sampling Theorem. Aliasing

8. Laplace Transform (LT)

8.1 Transfer function

8.2 SLITs described by differential equations, poles and zeros.

8.3 Block diagram and equivalent transfer functions

8.4 The unilateral LT

9. BODE's diagrams

 

 

 

Teaching Methodologies

The subjects of this course are presented both in theoretical and practical lectures using computer-aided contents whenever needed. The adopted methodology stimulates and privileges the active participation of students. The subjects are presented, discussed, and developed using problems and real situations. In order to consolidate the learning of the concepts, it is provided to students exercise series on each course topic, as well as all additional material to support lectures. 

Bibliography

Alan V. Oppenheim e Alan S. Willsky, Signals and Systems, Prentice-Hall.