Application of Two Frameworks-Physics and Signal Processing-As a Basis for Efficient Designs in Physical Computing

Abstract

This dissertation investigates the integration of physics and signal processing frameworks to advance efficient designs in physical computing, encompassing analog circuitry, neuromorphic, optical, and quantum systems. By leveraging the continuous nature of physical variables (characterized by ℵ₁ cardinality) in contrast to discrete (ℵ₀-based) digital systems, this work proposes a Physical-Computing Thesis, paralleling the Church-Turing Thesis, which highlights computational equivalences unique to physical systems and underscores that many physical computing phenomena cannot be fully and efficiently replicated by classical digital Turing machines. Drawing on a holographic principle, the thesis establishes correspondences between continuous and discrete signals and systems, revealing opportunities for superior computational efficiency. Key contributions include the identification of four types of Linear Time-Invariant (LTI) breaks, novel efficiency metrics, and their novel application to practical systems such as analog filters, differential pairs, synchronized chaotic circuits, and frequency synthesizers. My thesis demonstrates how physical computing can exploit nonlinearities and time-variance (what I call LTI-breaking) to achieve matter-energy-information efficiency, validated through my theoretical advancements and patented designs. By harmonizing historical insights from Faraday and Maxwell with modern signal processing, this work lays a foundation for future innovations in physical computing, challenging the limitations of the digital-centric paradigm.