Frequency Modulation and First-Order Delta Sigma Modulation: Signal Representation With Unity Weight Dirac Impulses

Signal representation by means of unity weight and continuous-time aperiodic Dirac impulses is discussed, where the Dirac impulses are triggered at the zero crossings of frequency-modulated (FM) sinusoids. Analysis is based on generalized FM. The Fourier spectrum Psi(f) of such a Dirac impulse sequence psi(t) is composed of the signal spectrum plus a superposition of weighted FM spectra around integer multiples of the carrier frequency. It is demonstrated that FM-related sequences Psi(t) are generated by asynchronous DeltaSigmamodulators of first order. Practically relevant clock-synchronous versions psi_d(t) of Psi_d(t) are obtained, when the clock rate is twice the FM carrier frequency. A DeltaSigma-spectrum psid(f) can be regarded as a superposition of weighted and shifted versions of psi(f), whereby the first partial FM spectrum in psi(f) around the FM carrier frequency plays a dominant role.