On the estimation of the spectrum of discrete pulsewidth modulated signals

The estimation of the spectrum of a pulse train modulated by a reference waveform in pulsewidth modulation (PWM) can be simplified if certain assumptions, based in the fact that the pulse train is generated in a discrete way, are taken into account. Sampling and quantization are applied both to the reference signal and to the PWM ramp leading to a simple method to calculate the Discrete Fourier Transform (DFT) of a PWM signal. This DFT can be used to estimate the Power Spectral Density (PSD) of the PWM signal. The estimation of the spectrum is a keystone of the design of the filter of a Buck converter used as Envelope Modulator in Envelope Tracking applications.