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This lecture covers the concept of Fourier series, focusing on the approximation of functions and their transformations. It explains how to use cosine and sine functions to represent periodic signals and discusses the properties of Fourier coefficients. The instructor demonstrates the process of transforming a function into its Fourier series and provides insights into the convergence of the series. Various examples and applications are presented to illustrate the practical use of Fourier series in signal processing and analysis.