This concept belongs to adaptive filtering theory within digital signal processing, specifically the block least-mean-squares (Block LMS) family of algorithms. It formalizes how a continuous data stream is partitioned into overlapping blocks so that both the filtering and weight-update recursions of an adaptive FIR filter can be computed via circular convolution (equivalently, DFT-domain multiplication) rather than direct time-domain convolution. A key structural theorem exploited here is a DFT-conjugation-and-flipping property: given a sequence's DFT, taking the conjugate of the DFT coefficients corresponds, in the time domain, to conjugating and reversing (flipping) the original sequence, which allows a single DFT computation to serve both the filtering step and the weight-update step, minimizing computational redundancy and unifying real- and complex-valued (Hermitian) extensions of the algorithm.
This concept belongs to adaptive filtering theory within digital signal processing, specifically the block least-mean-squares (Block LMS) family of algorithms. It formalizes how a continuous data str…