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
ELEE08021 Sensor Networks and Data Analysis 2 Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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