Research & Projects
Research Overview
My research lies at the intersection of pure and applied mathematics, with a focus on harmonic analysis and its applications to signal processing and frame theory.
I work in Applied Harmonic Analysis, exploring how mathematical tools such as Fourier series, Slepian series, frames, and wavelets can be used to represent, decompose, and reconstruct signals. A central theme in my work is the Gibbs Phenomenon — the behavior of function approximations near discontinuities — and how different methods can be used to mitigate it. My research bridges classical harmonic analysis with modern signal processing techniques.
Research Interests: Applied Harmonic Analysis · Frame Theory · Fourier Series · Slepian Series · Signal Processing
PhD Thesis
| Title | Approximation Theory and the Gibbs Phenomenon (not finalized) |
| Institution | University of Idaho |
| Expected | May 2027 |
| Advisor | Somantika Datta · Department of Mathematics and Statistical Science |
| Status | In Progress |
A well-known challenge in Fourier analysis is the Gibbs phenomenon — the persistent overshoot that occurs when approximating discontinuous functions using classical Fourier series. This thesis addresses this problem through the lens of approximation theory, introducing new series expansions as a mathematically rigorous alternative that reduces or eliminates this overshoot while preserving key signal features.
Current Research Projects
Mitigation Strategies for the Gibbs Phenomenon (Ongoing)
A systematic investigation of techniques designed to suppress or eliminate the Gibbs phenomenon — the persistent oscillations at the point of discontinuity that arise when approximating piecewise smooth functions via classical Fourier series. This project surveys and compares a range of mitigation approaches, from classical filtering and summability methods to modern frame-theoretic and spectral reprojection techniques, assessing their theoretical guarantees and practical effectiveness.
Topics: Fourier Analysis · Approximation Theory · Spectral Methods · Frame Theory
Approximating Discontinuous Functions via Prolate Spheroidal Wave Functions (Ongoing)
Exploring the use of Prolate Spheroidal Wave Functions (PSWFs) — a family of bandlimited functions with exceptional concentration properties — as an alternative basis for approximating functions with jump discontinuities.
Topics: Prolate Spheroidal Wave Functions · Bandlimited Approximation · Spectral Localization · Gibbs Phenomenon
Publications & Papers
📄 Publications coming soon. Research papers and preprints will be listed here as they become available.