Zak Transform Fundamentals: Signal and Time-Frequency Analysis

Time-frequency analysis provides powerful mathematical tools for analyzing non-stationary signals across physics, communications, and data engineering. This course introduces the Zak transform from the ground up, giving you a structured conceptual framework to work with dual time-frequency representations effectively. What you'll learn: Understand key definitions, quasi-periodicity, and fundamental properties of the continuous and discrete Zak transform. Analyze Gabor systems, frame theory, and sampling theorems through Zak-domain techniques. Apply transform methods to signal decomposition, inversion, and reconstruction problems. Connect theoretical concepts to modern applications in wireless communication, radar, and computational harmonic analysis. Practice analytical problem-solving through clear written explanations and structured mathematical exercises. The course begins with essential mathematical terminology and foundational linear algebra before guiding you through theoretical proofs, discrete formulations, and practical analytical workflows. This text-based guide is designed for beginners in advanced signal processing and applied mathematics with basic knowledge of calculus and linear algebra. Start reading today to master the foundations of the Zak transform.