Fourier Fitting Equation Implementation

This MATLAB program implements an automated curve fitting solution utilizing Fourier fitting equations. The script accepts a set of input data points and automatically computes the optimal fitting curve through Fourier series approximation. The implementation employs MATLAB's built-in curve fitting functions, likely using the fit function with 'fourier' model type, which generates a sum of sine and cosine terms to describe periodic patterns in the data. The algorithm works by determining the optimal Fourier coefficients that minimize the difference between the fitted curve and actual data points, typically using least-squares optimization methods. Key parameters such as the number of Fourier terms (fundamental frequency harmonics) can be automatically optimized or manually specified to balance between fitting accuracy and model complexity. This tool enables users to perform sophisticated data analysis and trend prediction by capturing cyclical patterns effectively. The program outputs the fitted equation parameters, goodness-of-fit statistics, and visualization of the original data versus fitted curve, facilitating informed decision-making based on quantitative analysis. Users can extend the functionality by incorporating confidence intervals, residual analysis, or custom Fourier term selection based on specific application requirements.