Spectral AIResearch GroupRU

Research

Shared tools do not imply shared guarantees. Each direction has its own mathematical assumptions, task definition and evaluation protocol.

01

Mathematical spectral analysis

Published

Problem

How do basis structure, function space and summation procedure govern approximation and the possible limits of an orthogonal expansion?

Methods

Walsh, Haar and generalized Walsh/Vilenkin representations; correction constructions, nonlinear greedy approximation and multiplier analysis.

Evidence & scope

Published work addresses uniform greedy convergence after small-set correction and universality of Walsh–Fourier partial sums. The multiplier review provides a separate operator-theoretic line.

Current questions

Which approximation and sampling guarantees survive changes of norm, weighting or dimension? How can compact spectral representations be designed without transferring infinite-dimensional claims to finite-data models?

Related work

On the uniform convergence of the greedy algorithm in a generalized Walsh systemUniversality properties of Walsh–Fourier seriesGreedy Approximation and Universal Functions by Generalized Walsh SystemsReview: Boundedness of Multiplier Operators in the Walsh SystemCompactness and Spectral Properties of Multiplier Operators in the Walsh System
02

Spectral representations & learning

Active research

Problem

Which retained transform summaries preserve task information while keeping their interpretation and sensitivity auditable?

Methods

Haar-scale summaries, Walsh coefficient-group energies, compact classifiers, training-only selection, reference deviations and feature-group explanations.

Evidence & scope

WHSDA-AI is published. HWSF is under revision with component-level bounds and controlled comparisons. Orthogonality preserves a full vector; pooling and selection change what the model observes.

Current questions

What remains stable after normalization, pooling and model fitting? How much morphology is lost under a common coefficient budget? Do explanations remain consistent under small input perturbations?

Related work

WHSDA-AI: Interpretable Walsh-Hadamard Spectral Deviation Analysis for Structured Artificial Intelligence Applications in Banking SectorStable Dyadic Spectral Fingerprints Based on Haar–Walsh Transforms for Discrete Signal and Data Analysis
03

Biomedical signals & ECG

Planned evaluation

Problem

Can compact prediction retain useful coverage when ECG acquisition, annotation alignment and beat detection are imperfect?

Methods

RR-only, waveform-only and combined models; matched Haar–Walsh/db4 representations, compact 1D CNNs, learned rejection, calibration and patient-grouped validation.

Evidence & scope

An executed six-record MIT-BIH software pilot revealed strong detector dependence and no demonstrated spectral advantage. SPECTRA EdgeMed plans the full grouped benchmark, frozen INCART evaluation and Raspberry Pi 5 measurements.

Current questions

Does learned quality rejection beat confidence rejection at matched coverage? What does morphology add beyond past RR? How do missed and false detections affect the complete operating envelope?

Related work

Stable Dyadic Spectral Fingerprints Based on Haar–Walsh Transforms for Discrete Signal and Data Analysis
04

Recovery of damaged signals

Research programme

Problem

Which signal properties permit recovery from missing samples or fragments, and where is reconstruction non-identifiable?

Methods

Proposed comparisons of spectral regularization, sparse or structured representations and corruption-aware evaluation, with explicit observation operators and recovery assumptions.

Evidence & scope

Research programme in development. No general reconstruction theorem or completed recovery benchmark is claimed on this site.

Current questions

How do gap geometry, observation density and noise level change attainable error? Can recovered morphology be validated against a withheld reference rather than only by visual plausibility?

05

Transforms, audio & information protection

Published

Problem

How do transform-domain processing and numerical implementation affect reversibility, signal statistics, cost and the analysis of hybrid schemes?

Methods

Walsh–Hadamard, Haar and DCT implementations; hybrid audio and text-processing experiments, numerical checks and explicit separation of statistical tests from cryptanalysis.

Evidence & scope

Published studies document software experience with audio transforms and hybrid AES/RSA schemes. Ciphertext entropy, correlation, NPCR and avalanche statistics alone do not establish cryptographic security.

Current questions

What follows from an explicit threat model and attack analysis? What are the effects of finite precision, key handling and invertibility? Which processing components are useful independently of security claims?

Related work

Hybrid audio encryption method based on DCT and Walsh-Hadamard transform using Henon chaotic maps and logistic mapsHYBRID AUDIO ENCRYPTION USING WALSH–HADAMARD TRANSFORM, HÉNON MAP, AND ADAPTIVE 3D LOGISTIC–SINE MAPEnhancing AES Security with the Integration of the Orthogonal Haar TransformHybrid Cryptographic Algorithm Based on Aes, Rsa and Walsh TransformSecure Data Handling: Performance Analysis of AES, Walsh Transform, and Hybrid Encryption

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.

Executed software pilotPlanned evaluation
Inside SPECTRA EdgeMed
Synthetic signal illustrationSynthetic / illustrative
01Acquisition
02Quality
03Prediction
04Evaluation