Fourier Series Expansion of Functions Using MATLAB
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In this document, we will implement Fourier series expansion of functions using MATLAB. Fourier series is a mathematical tool that decomposes periodic functions into sums of sine and cosine functions. By leveraging MATLAB's programming capabilities, we can efficiently compute and visualize Fourier series expansions through numerical integration techniques and symbolic math functions. The implementation typically involves calculating Fourier coefficients (a_n and b_n) using integral functions like int() or numerical methods, followed by reconstructing the series with summation operations. This approach helps analyze frequency spectrum characteristics and periodic behavior of functions, making MATLAB a powerful tool for signal processing applications. Key steps include defining the periodic function, specifying the number of harmonic components, and plotting original vs. approximated functions using MATLAB's graphical functions like plot() or fplot().
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