Fitting 1000 Sets of Complex Data with MATLAB Implementation

This article provides a comprehensive guide on implementing a crucial task in MATLAB: fitting 1000 sets of complex data and calculating the normalized mean square error (NMSE) of the fitting function. We begin by discussing fundamental fitting principles, including selection of appropriate fitting functions (such as polynomial, exponential, or custom models) and fitting algorithms (like least squares, nonlinear regression, or curve fitting toolbox methods). The implementation section demonstrates MATLAB code for data import using functions like 'load' or 'readmatrix', data preprocessing for complex numbers handling with 'real' and 'imag' functions, and performing actual fitting operations through built-in functions like 'fit' or 'polyfit' for complex data handling. We then illustrate NMSE calculation using MATLAB's matrix operations and statistical functions, explaining how NMSE = norm(y_actual - y_fitted)^2 / norm(y_actual)^2 provides crucial insights into fitting quality by normalizing error magnitudes. Through practical code examples and algorithm explanations, readers will gain proficiency in MATLAB-based data analysis and fitting techniques, enhancing their ability to leverage this powerful tool for complex numerical computations.