This thesis presents the theory and the experiment results with adaptive filtering algorithms. The experiments are based on the ultrawideband (UWB) Synthetic Aperture Radar (SAR) data. Several algorithms are investigated in this thesis such as Least Mean Square (LMS), Normalized Least Mean Square (NLMS), Leaky Least Mean Square (LLMS) and Recursive Least Square (RLS). First, the theory behind the above algorithms are briefly reviewed. Then, the experiments based on UWB SAR data are carried out. The aim is to design adaptive filters to cancel the unwanted noise present in SAR data as much as possible. The theory and experiments are started with the conventional LMS algorithm that is relatively simple for implementation and eligible to make an evaluation of the performance of the adaptive filter. The investigation is followed by NLMS, LLMS and finally RLS. The results achieved in this study also show that there is a gap between computer simulations and practical applications in applying the adaptive algorithms. For this reason, studies on using the adaptive algorithms for practical applications are still needed and therefore continued in the future.