An Algorithm for Sampling from Bandlimited Circular Probability Distributions

Abstract: In this Bachelor thesis, a novel algorithm for sampling from bandlimited circular probability distributions is presented. The algorithm leverages results from Fourier analysis concerning the Fejér kernel to simulate data with some desired probability distribution, realized as a sum of data sampled from a discrete distribution and a small continuous perturbation sampled from the Fejér kernel distribution. Relevant theory is presented before formally proving exact simulation using the algorithm. Experimental results confirm the validity of the theoretical results, and the efficiency of the algorithm is then compared with that of other sampling methods such as rejection sampling with a uniform envelope function.