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<p>In many practical applications, signals and environments are time varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify unknown systems. This paper investigates an adaptive filtering framework based on canonical systems with time-varying symmetric positive semidefinite Hamiltonian matrices. The proposed method adapts the Hamiltonian matrix using a gradient-based scheme designed to minimize the squared error between the system output and a desired reference signal. We establish theoretical stability guarantees via Lyapunov analysis, ensuring boundedness of system trajectories and convergence of the error signal under suitable assumptions. Furthermore, we present numerical integration schemes preserving the underlying Hamiltonian structure and projective techniques to maintain positive semidefiniteness of the Hamiltonian matrix. Extensive simulations on synthetic nonstationary signals illustrate the effectiveness and robustness of the proposed adaptive filter.</p>

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Adaptive filtering via canonical systems with time-varying hamiltonians

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Keshav Raj Acharya,
  • Pitambar Acharya

摘要

In many practical applications, signals and environments are time varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify unknown systems. This paper investigates an adaptive filtering framework based on canonical systems with time-varying symmetric positive semidefinite Hamiltonian matrices. The proposed method adapts the Hamiltonian matrix using a gradient-based scheme designed to minimize the squared error between the system output and a desired reference signal. We establish theoretical stability guarantees via Lyapunov analysis, ensuring boundedness of system trajectories and convergence of the error signal under suitable assumptions. Furthermore, we present numerical integration schemes preserving the underlying Hamiltonian structure and projective techniques to maintain positive semidefiniteness of the Hamiltonian matrix. Extensive simulations on synthetic nonstationary signals illustrate the effectiveness and robustness of the proposed adaptive filter.