The frequency spectrum of pulse width modulated signals

Authors:
Zukui Song;Dilip V. Sarwate
Affiliations:
Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL and Apogee Technology, Inc., 129 Morgan Drive, Norw ...;Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
Signal Processing - Special section: Security of data hiding technologies
Year:
2003

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Abstract

The determination of the frequency spectrum of a pulse width modulated (PWM) signal with general band-limited input x(t) has been an open problem for many years. We describe a new approach that gives exact analytical expressions for the spectra of uniform-sampling PWM signals and natural-sampling PWM signals with single-edge as well as with double-edge modulation. For the special case of single tone modulating signals, our results reduce to those obtained previously using a double Fourier series method. We also show that if the maximum magnitude of the derivative of x(t) is smaller than twice the carrier frequency, then a PWM signal consists of a baseband signal y(t) together with y(t) phase-modulated onto each carrier harmonic, where, for uniform-sampling PWM, y(t) is a nonlinear function of the modulating signal x(t), while for natural-sampling PWM, y(t) is just x(t) itself, that is, there is no distortion in the baseband when natural sampling is used.