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Signal Representation With Unity-Weight Dirac Impulses

A periodic and band-limited signal is represented by a periodic sequence of unity-weight Dirac impulses. If the signal contains B harmonics and the signal amplitude is below a particular limit, at least Dirac impulses within one period are required for signal representation. The spectrum of the impulses in the signal band is identical to the spectrum of the signal itself. A real-valued signal designated as “algebraic signal” can be associated with the input signal, whose zero crossings indicate the positions of the Dirac impulses. The relationship to a signal representation based on frequency modulation is investigated. From the analysis derived for periodic signals, a straightforward signal processing concept applicable to general signals is developed.