Signal Representation With Unity-Weight Dirac Impulses

摘要

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 $2{rm B}+1$ 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.