Foundations of Signals and Systems: Nyquist and System Stability

Understanding how continuous physical signals transition into the digital world is the cornerstone of modern engineering and digital signal processing. This course simplifies the core mathematical principles of signals and systems, focusing on sampling and stability.\n\nYou will transition from a basic understanding of mathematics to confidently calculating sampling rates, analyzing Nyquist intervals, and determining whether a discrete-time system is stable.\n\nWhat you'll learn:\n- Learn the foundational concepts of continuous and discrete-time signals\n- Calculate Nyquist rates and Nyquist intervals to prevent aliasing in digital systems\n- Understand the mathematical principles behind discrete system stability\n- Apply Z-transform basics to analyze system behavior in the Z-domain\n- Determine system stability using poles, zeros, and the unit circle\n- Practice solving numerical problems related to sampling and system response\n\nThis written course begins with essential definitions of signals, systems, and sampling. From there, you will explore the Nyquist-Shannon sampling theorem, learn how to calculate sampling intervals, and finish by analyzing discrete-time system stability using Z-domain techniques.\n\nThis course is designed for beginners in engineering, computer science, or digital signal processing who want a clear, step-by-step mathematical foundation. No advanced prerequisites are required.\n\nStart reading today to master the essential math behind modern digital signals.