On the rectangular transform approach for BLMS adaptive filtering

This paper presents a new Block Least Mean Squares(BLMS) adaptive filter structure by exploiting the use of an efficient circular convolution algorithm known as the rectangular transform(RT). The BLMS algorithm is presented as an approximation to a recursive block least squares (RBLS) algorithm. The analysis is used to develop the computationally superior overlap save adaptive filter structure even though the structure of the overlap add adaptive filter may be easily worked out in a similar manner. The computational requirements of the proposed filter are investigated and compared with an FFT based filter. The proposed filter is found to be a useful alternative to its FFT counterpart. For completeness, the convergence properties of the filter obtained from simulations are also included.