Signals and Systems

The course introduces basic concepts and properties of continuous-time and discrete-time signals and systems, and constitutes a core course in the department specialization area of signals, communications, and networks. In more detail, it covers the following: Elementary continuous- and discrete-time signals; convolution; continuous-time Fourier series and Fourier transform; discrete-time Fourier transform; sampling theorem; linear, time invariant systems, their description using differential / difference equations, as well as time and frequency analysis; Laplace transform; Z-transform; introduction to discrete Fourier transform; practical application of the above concepts to real-life signals and systems.

Objectives

This course introduces students to the basic concepts of the theory of signals and systems, both in the continuous-time and the discrete-time domain, also covering the main tools for their analysis in the time and frequency domains. The course also introduces signal sampling and reconstruction, while also providing numerous examples to allow student familiarization with the above concepts, as well as practical computational tools within the Matlab framework, further demonstrating these. The course constitutes a core one in the department specialization area / division of signals, communications, and networks. It allows students to gauge early on their studies their possible interest towards this direction, which they can further delve into by attending a number of relevant courses offered within the division, allowing them to pursue related careers. Students successfully completing this class will have mastered the main concepts, properties, and analysis tools of the field of signals and systems. For example, they will be able to: 1. Identify a number of basic continuous- or discrete-time signals, such as exponentials, sinusoids, unit steps and impulses, determine properties of given signals, such as periodicity, symmetry, and energy/power-type, and perform basic signal transforms in the time domain. 2. Determine whether systems are linear and time-invariant (LTI) and signify the importance of such class of systems. 3. Determine properties of LTI systems by a number of techniques in the time or transform domain, employing/selecting appropriate methods among ones based on the input-output relation, system impulse response, frequency response, or transfer function in conjunction with its region of convergence. 4. Calculate convolution sums and integrals. 5. Perform frequency analysis of a number of signals and stable LTI systems. 6. Perform signal sampling and reconstruction using appropriate parameters. 7. Describe practical electrical circuits and other physical systems within the course framework. 8. Utilize and implement Matlab programs to visualize and analyze signals and systems.

Prerequisites

Calculus I, Calculus II

Syllabus

The course covers topics that broadly characterize an introduction to the theory of signals and systems, their basic concepts, and tools for their analysis. In more detail, the following are covered: i. Elementary continuous- and discrete-time signals. ii. Properties of continuous- and discrete-time signals. iii. Properties of continuous- and discrete-time systems. iv. Linear, time-invariant (LTI) systems. v. Convolution sum and convolution integral. vi. Fourier series representations of periodic signals. vii. Continuous-time Fourier transform. viii. Discrete-time Fourier transform and discrete Fourier transform (introduction only). ix. Signal sampling and reconstruction. x. Examples of time and frequency domain analysis of LTI systems. xi. Examples of communication systems. xii. Laplace transform and continuous-time LTI system analysis using it. xiii. Z transform and discrete-time LTI system analysis using it. xiv. Basic computational tools in Matlab corresponding to the above.