Spectral decomposition is a mathematical technique that expresses a linear operator or matrix in terms of its eigenvalues and eigenvectors. This method allows complex systems to be analyzed by breaking them down into simpler, more manageable components, which is particularly useful in understanding periodic phenomena, like waves. By decomposing a function into its spectral components, one can analyze the contributions of each frequency, making it a crucial tool in various fields including signal processing and Fourier analysis.
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