Convolution Is Multiplication in the Fourier Basis
An interactive live film: the Fourier waves are eigenvectors of every circular convolution; drag the kernel and each wave is scaled by its eigenvalue until the alternating wave is erased.
Narration
A circular convolution with the kernel k zero, k one, k two is a matrix C built from the cyclic shift S. Here the signals have four entries.
The shift has eigenvectors that are waves. The four helices are the waves of frequency zero, one, two and three, drawn with their real and imaginary parts around the index axis.
The rest of the narration is in the book's Companion.
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