Signal processing is a discipline that encompasses various techniques for analyzing, characterizing, and studying signals.
The field of signal processing extends across several areas of engineering that require the understanding, transmission, and exploitation of information. Electronics and computer science are the two fields where signal processing is most commonly used, such as in telecommunications, detection, transmission, image processing, pattern recognition, instrumentation, meteorology, biomedical engineering, and other applications where signal processing is useful.
This course is intended for second-year electronics students and can be considered an introduction to signal processing. Its main objective is to introduce basic concepts and provide the necessary mathematical tools to highlight the main characteristics of a signal. To achieve this, the course is organized as follows:
The first chapter is considered an introduction to signal theory, where basic concepts such as common signals are introduced. Other concepts are discussed, such as signal classification and their time-domain description. We also focus on the various transformations that signals undergo and the determination of energy characteristics such as power and energy.
In the second chapter, the concept of spectrum is introduced. In the first section,
we specifically focus on periodic signals, where the spectrum is described using Fourier series. The three Fourier series developments (trigonometric, cosine, and complex) and their graphical representations are explained. At the end of this section, calculation examples are given to better understand the transition from one series to another and also to explain how to plot the amplitude and phase spectrums.
The second section of this chapter explain the concept of spectral analysis of nonperiodic signals using the Fourier Transform (FT). This transformation is a powerful tool for spectral description of signals, the properties of the FT are provided to facilitate the determination of the spectra of different signals.
In the third chapter, the concept of linear time-invariant systems is introduced. The
study of these systems is conducted through the convolution product. This product allows the description of a system’s response over time. We begin by developing the steps to determine the expression for the convolution product and its properties. Then, examples are provided to describe the two methods (analytical and graphical) for determining the convolution product of two signals.
The fourth chapter is dedicated to the study of systems in the frequency domain.
The transition from the time domain to the frequency domain is carried out through the Laplace Transform. We begin by defining the Laplace Transform, its properties, and some common transforms which allows the determination of the Laplace Transform of various signals. The second section of this chapter aims to determine the inverse Laplace Transform using either common transforms or by decomposing the function using the residue method. We conclude this chapter by providing some applications of the Laplace transform that are used to study systems. We conclude the course with a final chapter that briefly discuss the concept of signal correlation. We first define autocorrelation and cross-correlation for various classes of signals. Then, we define the energy spectral density, the properties of correlation, and the relationship between correlation and the convolution product.
- Teacher: BAHLOUL LIES