Design of One-Dimensional Wiener Filter

In this article, we will discuss the design of a one-dimensional Wiener filter. The implementation begins by generating three distinct sets of observation data, which can be created using MATLAB's random signal generation functions or predefined test signals. We will estimate their AutoRegressive (AR) model parameters through computational methods like the Levinson-Durbin recursion for solving Yule-Walker equations, which efficiently computes the filter coefficients. The analysis will focus on how signal length and model order affect experimental outcomes. For performance evaluation, key metrics including mean square error (MSE) and signal-to-noise ratio (SNR) improvements will be calculated. We will examine the trade-offs between computational complexity and filtering accuracy across different parameter combinations. Through these experiments, we gain deeper insights into Wiener filter performance and parameter selection strategies. The experimental process involves comparing filtering results under varying signal lengths and model orders, with optimization techniques such as cross-validation helping identify optimal parameter combinations. This comprehensive analysis from multiple perspectives provides a thorough understanding of Wiener filter applications and optimization methodologies for signal enhancement.