Foundations of Signal Processing

This course deals with engineering problems efficiently by developing a strong mathematical framework for the analysis of signals and systems. It introduces the fundamental concepts required to understand, model, and process signals encountered in modern electronic and electrical engineering applications. The course begins with the classification, representation, and properties of continuous-time and discrete-time signals, along with the basic concepts of systems and their classifications. A detailed characterization of Linear Time-Invariant (LTI) and time-varying systems is presented to enable systematic analysis of system behavior.

Key analytical tools such as convolution are introduced to determine system responses in the time domain, while Exponential Fourier Series and Fourier Transform techniques are employed for frequency-domain analysis of signals and systems. The course further covers essential transform methods, including the Laplace Transform and Z-Transform, which are widely used for system modeling, stability analysis, and design in both analog and digital domains. Fundamental concepts of signal sampling, reconstruction, aliasing, and the Sampling Theorem are also explored to establish the relationship between continuous-time and discrete-time signal processing.

The ideas and methodologies developed in this course form a strong foundation for advanced studies in control systems, communication systems, digital signal processing, statistical signal analysis, and digital image processing. By the end of the course, students will be equipped with robust analytical skills necessary to analyze and solve real-world engineering problems involving signals and systems.