Fundamentals Of Communication Theory – Unnikrishna Pillai

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Pillai, A. Patel, Fundamentals of Communication Theory https://doi.org/10.1007/978-3-032-20615-2_1 1. Fourier Series Unnikrishna Pillai1 and Anuj Patel2 Department of Electrical and Computer Engineering, New York University, New York, NY, USA Brooklyn, NY, USA Unnikrishna Pillai (Corresponding author) Email: [email protected] Anuj Patel Email: [email protected] Abstract This chapter provides the mathematical framework necessary for analyzing periodic signals in both time and frequency domains.

It begins with the foundational concepts that start with the Fourier Series representation of periodic signals. The focus here is on the representation of periodic signals using Fourier coefficients and the underlying principles such as Fourier’s Theorem, Parseval’s Theorem, and the Fourier Series expansion of real periodic signals. Along with theoretical development, key concepts with examples are illustrated, highlighting the importance of Gibb’s Phenomenon and real-world applications such as vibrato in music and Kepler’s equation.

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