Sliding transforms for efficient implementation of transform domain adaptive filters

An efficient technique for the implementation of the widely used orthogonal transforms when their input samples are originating from a tap delay line (TDL), and the transformation has to be performed after each new sample enters the TDL, is addressed. The redundancy in the input data samples is used to reduce the computational complexity of these transforms from order of N log N to order of N, where N is the length of transform. The term sliding is used to refer to such transforms. We use the Bruun's (1978) technique, to propose a number of sliding implementations for the most commonly used transforms. Our emphasis is on the transform domain adaptive filters which employ such transforms for decorrelating their input data.