MATLAB Source Code for Generating Discrete Gaussian Functions

This MATLAB source code generates discrete Gaussian functions, which are commonly used as digital filters obtained through discrete sampling of continuous Gaussian distributions. These functions play a vital role in digital signal processing applications such as noise reduction, edge detection, and image processing. The implementation utilizes an efficient algorithm that computes discrete Gaussian kernels by evaluating the Gaussian probability density function at integer grid points. The code ensures optimal performance and mathematical accuracy through proper normalization and sigma parameter control. Key functions include Gaussian kernel generation, sigma parameter validation, and kernel normalization routines. The algorithm works by first defining the kernel size based on the standard deviation parameter (sigma), then calculating Gaussian values at each discrete position, and finally normalizing the kernel to maintain energy conservation. This approach guarantees that the discrete Gaussian maintains its desirable properties including symmetry and smooth frequency response. If you require discrete Gaussian functions for digital signal processing tasks, this MATLAB implementation provides a reliable and computationally efficient solution. The code includes parameter customization options for different application requirements and validation checks to ensure mathematical correctness.