Power Spectrum Computation for an Arbitrary Phase Noise Using Middleton's Convolution Series: Implementation...

Area of Science:

• Physics
• Signal Processing
• Optical Engineering

Background:

• Phase noise power spectral density is crucial for understanding periodic signals in systems like lasers and oscillators.
• Existing methods for power spectrum calculation can be complex.

Purpose of the Study:

• To revisit and simplify the calculation of power spectrum from phase noise power spectral density.
• To provide a straightforward guideline for computing power spectra for arbitrary phase noise.
• To offer intuitive understanding of phase noise effects on spectral line shape.

Main Methods:

• Revisiting Middleton's convolution series for power spectrum analysis.
• Developing a simplified computational guideline for arbitrary phase noise.
• Applying the method to experimental signals with varying phase noise levels.

Main Results:

• A straightforward method for computing the power spectrum from phase noise power spectral density was introduced.
• The approach demonstrated computational benefits.
• Excellent agreement was observed between computed and experimental spectra across different phase noise regimes.

Conclusions:

• The revisited convolution series offers an intuitive and computationally efficient way to determine the power spectrum of periodic signals.
• This method is broadly applicable to scientific areas involving lasers and oscillators.
• The approach enhances understanding of phase noise impacts on spectral characteristics.