Spectral Analysis of Pulsewidth-Modulated Sampled Signals

Pulsewidth (PW) modulation has been widely used to convert analog (or multibit digital) signals to binary streams. It is well known that PW modulation of a sampled signal produces harmonic distortion. This effect is analyzed, and new expressions are obtained for the Fourier transform of the modulated output, which are valid for any input signal. In addition, simple expressions are given to compute the harmonic distortion factors for a sinusoidal input signal. It is also shown that a three-level PW modulation can reduce the distortion factors down to a level appropriate for most signal-processing applications. Finally, these analytical results are validated by simulation for two data converters based on sigma-delta modulation, where the sampled output of a multibit quantizer is PW modulated: one digital-to-analog and one analog-to-digital converter, respectively.