Generation of random sequences with jointly specified probability density and autocorrelation functions.

Area of Science:

• Signal Processing
• Probability Theory
• Numerical Simulation

Background:

• Generating random sequences with specific statistical properties is crucial for various scientific applications.
• Existing methods may struggle with simultaneously controlling both probability distribution and auto-correlation functions, especially for non-Gaussian data.

Purpose of the Study:

• To present a new, versatile method for generating stochastic sequences with user-defined first-order probability distribution functions (PDF) and auto-correlation functions (ACF).
• To provide a technique applicable to generating experimental stimuli and test data for signal processing and system identification.

Main Methods:

• Generation of numbers conforming to the desired PDF.
• Modification of the auto-correlation function to a white (independent) state using double stochastic interchange.
• Stochastic shuffling of the sequence to achieve the target ACF by minimizing a sum of squares criterion.

Main Results:

• Successfully generated stochastic sequences with arbitrarily specified first-order PDF and ACF.
• Demonstrated the method's effectiveness in producing colored, non-Gaussian data.

Conclusions:

• The presented method offers a robust approach for creating complex stochastic sequences.
• This technique is valuable for applications requiring non-white, non-Gaussian data, such as system identification and signal processing algorithm testing.