MATLAB Code Implementation for Gaussian Fitting

Gaussian fitting is a data fitting methodology primarily employing Gaussian functions to approximate datasets. The Gaussian function, a fundamental mathematical model, effectively describes numerous natural phenomena and statistical distributions. Through Gaussian fitting procedures, we can extract key parameters including the mean (center position) and variance (spread) of the fitted Gaussian curve. These parameters are essential for analyzing data distribution characteristics and identifying underlying patterns. In MATLAB implementation, Gaussian fitting typically involves using the curve fitting toolbox with fittype('gauss1') for single-term Gaussian models or custom implementations using optimization algorithms like lsqcurvefit. The core algorithm minimizes the sum of squared residuals between the empirical data and the Gaussian model, often employing nonlinear least-squares optimization techniques. Key functions include defining the Gaussian equation: f(x) = a*exp(-((x-b)/c)^2), where parameters a, b, c represent amplitude, mean, and standard deviation-related values respectively. Furthermore, Gaussian fitting finds extensive applications in signal processing and image analysis domains. By convolving signals or images with Gaussian kernels, we can extract crucial feature information, which is vital for tasks like data analysis and pattern recognition. MATLAB's imgaussfilt function exemplifies this application for image smoothing and feature enhancement using Gaussian filters.