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4. Fourier transform
We now turn to the Fourier transform, the very basis of modern harmonic analysis. We are still working in the space
, although in practice we often have N = 1; our notations, however, are designed to make very little difference to this simpler case (see the paragraph on notations): for there is no additional difficulty in the general case.
The Fourier transformation makes extensive use of the complex exponential, so it's worth recalling its basic properties. The exponential...
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Fourier transform
Fourier series
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