Source Code for Common Higher-Order Statistics Functions

This article provides comprehensive details about common higher-order statistics functions, including their fundamental usage scenarios. We present MATLAB source code implementations with enhanced technical descriptions for various applications: parametric model-based higher-order spectrum estimation (utilizing autoregressive and moving average models), linear prediction algorithms (employing Levinson-Durbin recursion), harmonic signal recovery and Direction of Arrival (DOA) estimation techniques (using MUSIC and ESPRIT algorithms), nonlinear stochastic process analysis (implementing Volterra series and bilinear models), Wigner-Ville distribution for time-frequency analysis (with cross-term suppression methods), and time delay estimation approaches (based on higher-order cumulants and cross-correlation techniques). Each code section includes implementation details explaining key algorithmic steps, such as cumulant calculation methods, matrix operations for spectral estimation, and optimization techniques for parameter estimation. Additionally, we provide comprehensive usage guidelines describing input/output parameters, configuration options, and practical application scenarios to help users better understand the functionality and implementation specifics of these higher-order statistical functions. We hope this resource assists researchers and engineers in effectively applying these advanced statistical methods to their signal processing projects.