This paper aims at the obliteration of noise signals such as echo, random, background and pink noise from speech signals such as FM, CD, Auditorium and Teleconference by deploying adaptive filters. The canceller of the filter uses a few adaptive algorithms such as RLS (Recursive Least Mean Square), LMS (Fast Least Mean Square) and FxT-RLS (Fast Sectional Convolution Transversal Recursive Least Square). The FxT-RLS Algorithm is implemented by using a traversal structure for the sectional convolution FFT in F-RLS. In this method the signals are converted to their frequency domain by taking their FFT using a traversal structure. In RLS and LMS algorithm, a feedback loop is utilized but in FxT-RLS, blocks are used in the adaptive filter. These algorithms use FIR filters with taps, which are preferred to diminish the error signal emanating from the system where minimization of the errors are based on the stochastic gradient method. The noise signal and the algorithm are implemented in TMS320C6713.These algorithms are based on the following criteria: i) stability ii) complexity iii) Signal-to-Noise Ratio (SNR) iv) Bit Error Rate (BER) v) Convergence Speed. Here, the comparison of all the algorithms is carried out and based on the above parameters FxT-RLS algorithm is found to be better than other two.