A q-deformed deterministic gradient framework generalizing affine projection adaptive filters

Purpose This work proposes a q-deformed deterministic gradient framework that generalizes affine projection adaptive filters by embedding a deformation of the classical gradient operator into a fully deterministic formulation. Design/methodology/approach By embedding the q-gradient into an affine projection–like structure, we derive a closed form update that preserves projection geometry while incorporating a feature-wise diagonal correction controlled by q. Findings The resulting deterministic q-APL recursion eliminates probabilistic assumptions and is specifically designed for coherent periodic disturbances. Originality/value We present a new deterministic q-APL algorithm for adaptive filtering. Experimental results on demonstrate that the proposed framework achieves strong attenuation of periodic interference, preserves waveform structure, and maintains convergence properties comparable to stochastic adaptive algorithms under both nominal and distorted interference conditions.