Signal and System for Students

This course provides a comprehensive introduction to the fundamental principles and mathematical frameworks required for the analysis, modeling, and design of engineering systems that process signals. It is designed to build a strong conceptual and analytical foundation by systematically exploring how signals are represented, transformed, and manipulated in both continuous-time and discrete-time domains. The course begins with the classification and description of signals, including deterministic and random signals, periodic and aperiodic signals, energy and power signals, and continuous-time versus discrete-time representations.

Students then learn how systems are modeled using differential equations for continuous-time systems and difference equations for discrete-time systems. A major emphasis is placed on linear time-invariant (LTI) systems, as they form the backbone of most practical engineering applications. Fundamental system properties such as linearity, time invariance, causality, memory, and stability are studied in detail to enable rigorous system characterization and analysis. The concept of convolution is introduced as a powerful tool for determining system responses in the time domain.

The course further develops frequency-domain analysis techniques through the study of Fourier series and Fourier transform, enabling students to understand spectral representations of signals and system behavior. Advanced transform methods, including the Laplace transform and Z-transform, are covered to facilitate system analysis, stability assessment, and design in more complex scenarios. Throughout the course, equal emphasis is placed on both time-domain and frequency-domain perspectives, supported by practical examples and problem-solving exercises. By the end of the course, students will be well prepared for advanced studies in communications, control systems, digital signal processing, electronics, and other related engineering disciplines.