#12 Fourier Integral Theorem - Informal Proof | Transform Techniques for Engineers

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This lecture extends the concept of Fourier analysis to non-periodic functions, which are defined over the entire real line. It presents the Fourier integral theorem, which provides a way to represent non-periodic functions as a continuous sum of complex exponentials. The theorem is derived by linking it to the Fourier series representation of periodic functions. The lecture emphasizes the conditions for the validity of the theorem, requiring the function to be piecewise smooth and absolutely integrable over the entire real line.
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#FourierIntegralTheorem #NonPeriodicFunctions #PiecewiseSmoothFunctions #AbsolutelyIntegrableFunctions