Fourier Transform
Analysis_and_Synthesis_Fourier_Transforms.jpg

let $L \rightarrow \infty$
$f(x) = \int_0^{\infty}[A(w)cos wx+B(w)sin wx]dw=\frac{1}{\pi}\int_0^{\infty}\int_{-\infty}^{\infty}f(v)cos(wv-wx)dvdw$
$A(w) = \frac{1}{\pi}\int_{-\infty}^{\infty}f(v)cos wv dv$
$B(w) = \frac{1}{\pi}\int_{-\infty}^{\infty}f(v)sin wv dv$

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