Digital simulation of an arbitrary stationary stochastic process by spectral representation

Area of Science:

• Signal Processing
• Computational Physics
• Statistical Modeling

Background:

• Generating discrete samples with specific probability density functions (PDFs) and spectral content is crucial for simulations.
• Existing methods often rely on complex autoregressive or iterative techniques, limiting efficiency and applicability.

Purpose of the Study:

• To present a computationally fast and straightforward method for synthesizing discrete samples with arbitrary PDFs and specified spectral content.
• To demonstrate the efficacy of a single inverse transform application for achieving accurate simulations.

Main Methods:

• Transforming white noise (Gaussian distributed) samples to match a desired spectral distribution.
• Applying an inverse transform to the spectrally shaped Gaussian distribution to achieve the target PDF.
• Analyzing the accuracy and limitations of the single-application inverse transform method.

Main Results:

• A single inverse transform application yields satisfactory results for a wide range of arbitrary PDFs and target power spectra.
• The method is computationally efficient and fast, suitable for generating large sample sets.
• While not perfectly conserving power spectra, the method provides accurate engineering approximations for system simulations.

Conclusions:

• The presented method offers an efficient and accurate approach for simulating random processes with desired statistical and spectral properties.
• The technique is applicable to a broad range of probability distributions and power spectra, with demonstrated relevance in optics.
• The method shows potential for extension to non-stationary random processes.