Adaptive filters play an important role in modern day signal processing with applications such as noise cancellation, signal prediction, adaptive feedback cancellation and echo cancellation. The adaptive filters used in our thesis, LMS (Least Mean Square) filter and NLMS (Normalized Least Mean Square) filter, are the most widely used and simplest to implement. The application we tested in our thesis is noise cancellation. A detail study of both filters is done by taking into account different cases. Broadly test cases were divided into two categories of stationary signal and non-stationary signal to observe performance against the type of signal involved. Noise variance was another factor that was considered to learn its effect. Also parameters of adaptive filter, such as step size and filter order, were varied to study their effect on performance of adaptive filters. The results achieved through these test cases are discussed in detail and will help in better understanding of adaptive filters with respect to signal type, noise variance and filter parameters.