Sin and Cos Functions as Sums and Difference of Complex Exponential - Derivation of Formulas

Published: 19 November 2023
on channel: Aleksandar Haber PhD

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In this mathematics, calculus, signal processing, and control engineering tutorial, we will learn how to express sin and cos functions of the real argument or of the real angles as the sum and difference of complex exponentials. The formulas derived in this video tutorial are of fundamental importance in digital signal processing, control engineering, and in many other fields because many times they can be used to significantly simplify calculations of quantities such as transfer functions, magnitude and phase responses, etc. In this tutorial, we explain how to derive these formulas, and at the end of the tutorial, we explain how these formulas can be used to compute the coefficients of the Fourier series Expansion.

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