Linear Time Invariant LTI Systems Linearity Property with Examples

Causal and non-causal systems course, in this course offers an in-depth exploration of causality in system design and analysis. Starting with fundamental definitions, you'll learn how causal systems depend solely on present and past inputs, making them suitable for real-time applications, unlike non-causal systems that rely on future inputs and are primarily theoretical or used in offline analysis. The course covers applications across fields such as signal processing, control systems, and data modeling, where causality plays a crucial role in determining system functionality. Practical examples will illustrate how causal systems are integral to digital filters and real-time control systems, while non-causal systems find use in predictive modeling and post-processing in image and audio analysis. Through exercises and simulations, you’ll understand the mathematical foundations of causality, causal and non-causal filter design, and stability requirements. By the end, you’ll have a solid grasp of how to identify, design, and apply both types of systems effectively across various engineering contexts.