1993/02/18 by Jayakumar Ramanathan, Ramanathan, Jayakumar, Pankaj Topiwala +1
Computer Science · Earth and Planetary Sciences · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Underwater Acoustics Research #funct-an #math.FA
paper · pdf · doi:10.48550/arxiv.funct-an/9302004
14 pages, LaTeX
arxiv created 1993/02/18 · openalex publication_date 1993/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a translate of a fixed window. The problem of finding signals with Gabor transform that are maximally concentrated within a given region of phase space is discussed. It is well known that such problems give rise to an eigenvalue problem for an associated self-adjoint, positive \em concentration operator that has its spectrum contained in the unit interval. In this paper, the asymptotic behavior of these eigenvalues as the concentration region gets large is studied. The smoothness of the eigenfunctions is also examined.