An adaptive signal processor using a Newton/least mean square (LMS) algorithm, adapted to remove a signal distortion or noise. The adaptive signal processor is adapted to derive an autocorrelation matrix from an input signal, derive an inverse matrix of the autocorrelation matrix by executing DCT twice or executing DFT and IDFT, and apply the derived inverse matrix to an adaptive signal processing, thereby capable of greatly reducing the total amount of computations to derive the inverse matrix, achieving an easy hardware realization thereof and reducing the manufacture cost thereof.