Let's say I know the Fourier transform of a function that is $0$ outside some interval, for example a triangle wave. How can this be used to find the Fourier series of the related periodic function, in this case a train of triangle waves?
How can the FT be used to find the FS of the periodized signal?
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fourier-analysis
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1We have the following result: "If $f(t)$ is an integrable function with fourier transform $F(\omega )$ and $T$ is a positive constant,then $\sum _{i=-\infty }^{\infty } f(t+\text{iT})$ is also an integrable function with *nth* fourier coefficent $\frac{1}{T}F\left(\frac{n}{T}\right)$. Note that the new function is $T$ periodic and i guess is your "the related periodic" function – 2011-12-12