Mathematical spectral analysis
PublishedApproximation, universality and operators in dyadic systems.
SPECTRAL METHODS · MATHEMATICS · AI
Spectral AIFrom mathematical structure
to testable AI.
We study dyadic spectral methods, interpretable representations and compact learning systems. Our work connects rigorous analysis with signal experiments that expose both useful behaviour and operating limits.
- 01Mathematical foundations
- 02Spectral representations
- 03Learned models
- 04Signal evaluation
- 05Reproducible implementation
Research
One method can connect fields.
A claim still needs its own evidence.
Five research directions, with their methods, results and open questions stated separately.
Spectral representations & learning
Active researchInterpretable signed contrasts and multiscale descriptors.
Biomedical signals & ECG
Planned evaluationQuality, calibration and complete processing cost.
Recovery of damaged signals
Research programmeMissing samples, corruption and recoverability limits.
Transforms, audio & information protection
PublishedTransform implementations and qualified security evaluation.
Current project / SPECTRA EdgeMed
What happens when the detector is imperfect?
SPECTRA EdgeMed examines compact ECG models together with signal quality, selective prediction and complete device cost. A working software pilot motivates the planned patient-grouped and external evaluation.
Inside SPECTRA EdgeMedSynthetic / illustrative
01Acquisition
02Quality
03Prediction
04Evaluation
Selected results
These are scoped summaries; consult the cited paper for the full theorem and hypotheses.
Published mathematical result
Greedy convergence after correction
For generalized Walsh systems Ψₐ with integer a ≥ 2, the 2013 paper studies uniform greedy convergence after changing a function on a set of small measure. The correction assumption is essential to the statement’s scope; this is not a claim for every unchanged function.
On the uniform convergence of the greedy algorithm in a generalized Walsh systemPublished mathematical result
Large families of limit functions
The 2014 joint paper with Jürgen Müller establishes maximal families of limit functions for Walsh–Fourier series of W-continuous functions on small subsets of [0,1]. Both the W-continuity setting and the restriction to small sets belong to the result.
Universality properties of Walsh–Fourier seriesPublished method & experiments
Auditable signed-contrast representations
WHSDA-AI associates selected Walsh coefficients with documented feature-group comparisons and versioned explanation cards. The contribution is representation and governance within a supervised pipeline; an unselected orthogonal transform cannot improve Euclidean rankings.
WHSDA-AI: Interpretable Walsh-Hadamard Spectral Deviation Analysis for Structured Artificial Intelligence Applications in Banking SectorThe people behind the methods
Four researchers with complementary responsibilities in analysis, data audit, learning and embedded implementation.
Scientific lead
Sergo A. Yepiskoposyan
Professor · Doctor of Physico-Mathematical Sciences
ORCIDData audit & reproducibility
Svetlana A. Grigoryan
Doctoral researcher
Signal quality & embedded systems
Spartak S. Sirakanyan
MSc
Compact AI & model evaluation
Davit S. Hovhannisyan
MSc