A performance bound on low-pass reconstruction from PWM signals

A performance bound on low-pass reconstruction of a finite energy, band-limited signal from its corresponding pulse width modulated (PWM) signal is given. A finite dimensional input signal structure is proposed and its characteristics such as ℒ∞ norm and convergence rate in the tail regions are investigated. The criteria on sampling rate and reference signal structure for lossless PWM generation are specified. With uniform oversampling, different PWM structures are constructed using a generator consisting of an ideal sampler and a comparator. An equivalent model for PWM generation and low-pass reconstruction is proposed in order to separate infinite energy components in the modulated signal from the finite energy information bearing components. Using the equivalent model, bounds on distortion energies due to low-pass reconstruction and the corresponding signal to distortion ratios are given. Characteristics of low-pass reconstruction from different PWM signals such as output shifts, blurring effects and distortion attenuations are discussed.