{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T09:51:30Z","timestamp":1768557090582,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T00:00:00Z","timestamp":1768435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electronics"],"abstract":"<jats:p>Adaptive filtering remains a cornerstone of modern signal processing but faces fundamental challenges when confronted with rapidly changing or nonlinear environments. This work investigates the integration of deep learning into adaptive-filter architectures to enhance tracking capability and robustness in non-stationary conditions. After reviewing and analyzing classical algorithms\u2014LMS, NLMS, RLS, and a variable step-size LMS (VSS-LMS)\u2014their theoretical stability and mean-square error behavior are formalized under a slow-variation system model. Comprehensive simulations using drifting autoregressive (AR(2)) processes, piecewise-stationary FIR systems, and time-varying sinusoidal signals confirm the classical trade-off between performance and complexity: RLS achieves the lowest steady-state error, at a quadratic cost, whereas LMS remains computationally efficient with slower adaptation. A stabilized VSS-LMS algorithm is proposed to balance these extremes; the results show that it maintains numerical stability under abrupt parameter jumps while attaining steady-state MSEs that are comparable to RLS (approximately 3 \u00d7 10\u22122) and superior robustness to noise. These findings are validated by theoretical tracking-error bounds that are derived for bounded parameter drift. Building on this foundation, a deep-learning-driven adaptive filter is introduced, where the update rule is parameterized by a neural function, U\u03b8, that generalizes the classical gradient descent. This approach offers a pathway toward adaptive filters that are capable of self-tuning and context-aware learning, aligning with emerging trends in AI-augmented system architectures and next-generation computing. Future work will focus on online learning and FPGA\/ASIC implementations for real-time deployment.<\/jats:p>","DOI":"10.3390\/electronics15020381","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T14:35:38Z","timestamp":1768487738000},"page":"381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Deep-Learning-Driven Adaptive Filtering for Non-Stationary Signals: Theory and Simulation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8872-5721","authenticated-orcid":false,"given":"Manuel J. Cabral S.","family":"Reis","sequence":"first","affiliation":[{"name":"Engineering Department and IEETA, University of Tr\u00e1s-os-Montes e Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Widrow, B., and Hoff, M.E. (1960, January 23\u201326). Adaptive Switching Circuits. 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