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Line 45: whose [[Fourier transform]] is just''':''' :<math>\begin{align} ~~:<math>~~W_0(f) &= \tfrac{1}{2}\frac{\sin(\pi Lf)}{\pi f} + \tfrac{1}{4} \frac{\sin(\pi L(f-1/L))}{\pi (f-1/L)} + \tfrac{1}{4} \frac{\sin(\pi L(f+1/L))}{\pi (f+1/L)}~~.</math>~~\\ &= \frac{L}{2\pi}\left( \frac{\sin(\pi Lf)}{Lf} -\tfrac{1}{2} \frac{\sin(\pi Lf))}{Lf-1} -\tfrac{1}{2} \frac{\sin(\pi Lf))}{Lf+1}\right)\\ &= \frac{L\sin(\pi Lf)}{2\pi}\left(\frac{1}{Lf} +\tfrac{1}{2} \frac{1}{1-Lf} -\tfrac{1}{2} \frac{1}{1+Lf}\right)\\ &= \frac{L\sin(\pi Lf)}{2\pi}\left(\frac{1}{Lf (1-Lf) (1+Lf)}\right). \end{align}</math> == Discrete transforms ==

Hann function: Difference between revisions