= Periodic extension of a finite sequence
{title2=$x_{n+N}=x_n$}
A block $x_0,\ldots,x_{N-1}$ determines a repeating <sequence> by setting $x_n=x_{n\bmod N}$ for every <integer> $n$. The <inverse discrete Fourier transform> gives this extension because each <discrete Fourier mode> satisfies $e^{2\pi ik(n+N)/N}=e^{2\pi ikn/N}$. The extension explains why <circular convolution> wraps indices around the block. It specifies values at discrete indices; a continuous curve between samples requires an additional choice of <interpolation>.
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