MATLAB Function for Generating Alpha-Stable Distributed Signals

This documentation presents a MATLAB function designed to generate alpha-stable distributed signals. The function is particularly effective for simulating noise signals exhibiting sharp spikes and heavy-tailed distributions. Alpha-stable distribution is a statistical model capable of representing random variables with highly flexible tail behaviors and peak characteristics. The implementation utilizes the Nolan's parameterization method, where the function accepts four key parameters: alpha (characteristic exponent), beta (skewness), gamma (scale), and delta (location). The function employs the Chambers-Mallows-Stuck method for random variable generation, which combines multiple independent random variables through trigonometric transformations to produce stable-distributed samples. Key algorithm steps include: 1. Generating independent uniform and exponential random variables 2. Applying trigonometric transformations based on the alpha parameter 3. Scaling and shifting results according to gamma and delta parameters 4. Handling special cases for alpha=1 and alpha=2 (Gaussian case) This function is particularly valuable in signal processing and communications research, as it enables researchers to simulate and analyze noise signals with impulsive characteristics. The generated signals can be used for testing robust signal processing algorithms, evaluating communication system performance under impulsive noise conditions, and developing spike detection methods. For researchers needing to model and study signals with heavy-tailed distributions and impulsive behavior, this MATLAB function provides an efficient and reliable simulation tool. The function includes parameter validation and error handling to ensure proper usage across different parameter ranges.