Ant Colony Optimization (ACO) algorithms belong to class of Meta-heuristic algorithms, where a search is made for optimized solution rather than exact solution, based on the knowledge of the problem domain. ACO algorithms are iterative in nature. As the iteration proceeds, solution converges to the optimized solution. In this paper, we examine the pheromone trial, a knowledge repository for ants, which guides the ants in the search process and analyzed the nature of convergence of ACO algorithms using Fourier transforms.