Description:SpectralONN is a novel neural architecture that learns directly in the frequency domain using phase-aware real and imaginary operator blocks, bounded by spectral norms. It applies magnitude-based activation for stability, supports modular ablation, and enables interpretable, hardware-free signal classification—ideal for biomedical and real-time spectral applications.
Core Principle:
The invention, SpectralONN, is grounded in the principle of learning in the frequency domain rather than the traditional spatial domain. It decomposes time-series signals—such as ECGs—into their Fourier or Chebyshev spectral representations, and models these using real-valued, phase-aware linear operators that act separately on the real and imaginary parts of the transformed input. The model avoids unstable complex-valued nonlinearities by projecting these outputs back into the magnitude space, yielding robust and interpretable representations. Each layer of SpectralONN is designed as a bounded linear operator, enabling rigorous analysis of stability and smoothness through operator norms and Lipschitz continuity. This design brings together ideas from classical signal processing and modern deep learning, offering a principled, explainable architecture for spectral neural learning.
, C , C , Claims:We claim:
1. A system for frequency-domain signal classification using bounded spectral operator learning, comprising:
a. A spectral transformation module configured to convert time-domain input signals into frequency-domain representations using either a Fourier or Chebyshev basis;
b. A real-imaginary decomposition unit that separates the transformed signals into real and imaginary components;
c. A spectral operator projection module comprising learnable linear operators that independently process real and imaginary components;
d. A magnitude-based activation unit that computes spectral energy to ensure phase invariance and model stability;
e. A classification module that maps the activated outputs to target classes using a fully connected layer.

2. A method for training and evaluating a modular spectral neural network, comprising:
a. Transforming input signals using a selected spectral basis (Fourier or Chebyshev);
b. Decomposing the spectral output into real and imaginary parts for independent operator learning;
c. Applying bounded real-valued linear operators to each component and activating the result using spectral magnitude computation;
d. Training the system with classification loss and evaluating model performance using accuracy, confusion matrix, and spectral evolution plots.
3. The system of claim 1, wherein the spectral operator projection module applies bounded linear transformations constrained by Lipschitz continuity to enhance stability and interpretability.
The method of claim 2, wherein spectral operator stability is evaluated using singular value spectrum analysis and operator norm estimation.
4. The system of claim 1, further comprising a modular ablation controller allowing configuration of:
a. A full SpectralONN variant with phase-aware learning;
b. A magnitude-only SpectralONN variant excluding phase components;
c. A Chebyshev SpectralONN variant using Chebyshev basis for localized spectral modeling.

5. The method of claim 2, wherein training includes evaluation of ablation variants to quantify the impact of phase and basis selection on model generalization.
6. The system of claim 1, wherein the spectral transformation module supports real-time signal processing for biomedical, synthetic, or vibration-based time-series data.
7. The method of claim 2, further comprising visual diagnostics including:
a. Spectral evolution plots showing frequency-domain feature refinement across layers;
b. Heatmaps of learned spectral operator weights;
c. Singular value plots comparing real and imaginary operators.
8. The system of claim 1, wherein the classification module is optimized for deployment on software-only, hardware-independent platforms, including cloud notebooks, edge AI devices, and research environments.
9. The method of claim 2, wherein model performance is benchmarked against spatial-domain neural baselines using accuracy, loss, and confusion matrix comparison.