This Topic introduces the concept of the impulse train, a sequence of Dirac delta impulses, which can be used to perform regular sampling of a signal. The impulse train is fundamental to Nyquist sampling theory, and has a number of powerful and interesting properties. First, it is a periodic signal, and therefore can be analysed using the Fourier series. Second, the complex Fourier coefficients are all constant value, therefore effectively having a flat spectrum. This leads to the infamous Poisson's summation formula. Consequently, it can be shown that the Fourier transform of an impulse train is itself an impulse train, and therefore an eigenfunction of the Fourier transform operator.


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