Introduction to Signals and Systems: Continuous and Discrete Time

Understanding how signals are represented, transformed, and processed is the foundation of modern engineering, communications, and data science. This course clarifies the complex mathematical concepts behind both continuous-time and discrete-time systems. You will transition from basic mathematical definitions to analyzing linear time-invariant (LTI) systems and applying frequency-domain transformations. By reading through clear explanations and working through guided analytical exercises, you will develop a strong intuitive and mathematical grasp of how signals behave in the real world and in digital devices. What you'll learn: - Understand the fundamental classifications of continuous-time and discrete-time signals and systems. - Analyze Linear Time-Invariant (LTI) systems using convolution sum and convolution integral methods. - Apply Fourier analysis to represent signals in the frequency domain. - Explore the Laplace transform and Z-transform for system analysis and stability testing. - Relate classic signal processing theory to modern digital applications and software-based filtering concepts. The journey begins with foundational definitions of signal properties, moving systematically through system characteristics, convolution, and frequency-domain representations. You will progress from continuous-time theories to discrete-time applications, ensuring a complete conceptual framework. This text-based course is designed for undergraduate students, aspiring engineers, and self-taught learners looking for a structured introduction to signal processing. No prior exposure to signals and systems is required, though a basic background in calculus is helpful. Start building your foundational knowledge of signals and systems today.