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Power Spectrum Computation for an Arbitrary Phase Noise Using Middleton’s Convolution Series: Implementation Guideline and Experimental Illustration

In this paper, we revisit the convolution series initially introduced by Middleton several decades ago to determine the power spectrum (or spectral line shape) of a periodic signal from its phase noise power spectral density. This topic is of wide interest, as it has an important impact on many scientific areas that involve lasers and oscillators. We introduce a simple guideline that enables a fairly straightforward computation of the power spectrum corresponding to an arbitrary phase noise. We show the benefit of this approach on a computational point of view, and apply it to various types of experimental signals with different phase noise levels, showing a very good agreement with the experimental spectra. This approach also provides a qualitative and intuitive understanding of the power spectrum corresponding to different regimes of phase noise.