Abstract: This thesis deals with design and analysis of both fullband and subband adaptive filters and compared between them with applications in real speech. . The Normalized Least Mean Square (NLMS) algorithm has been used to make control an adaptive filter. In fullband adaptive filter the system shows slow convergence time compared with subband adaptive filter with lower signal to noise ratio is gave about 0.00003 noise reduction with (S/N) = 3.24 dB according to woman voice and gave 0.000015 with (S/N) =3.68 dB according to man voice when both tested with real speech. In subband adaptive filter in noise cancellation using subband filter banks. The input noisy speech is divided into number of bands by using filter bank and this noisy speech passes into a number of channels to get faster convergence time and high signal to noise ratio gave about 0.006 noise reduction with (S/N) = 10.314 dB according to woman voice and gave about 0.001 noise reduction with (S/N) = 11.2 dB according to man voice when tested with real speech. Although sample frequency can be used in subband is equal or greater than fulband. The simulations presented in this thesis are performed using MATLAB software package ver.7 operating under Microsoft Windows .