The Eigenvalue Distribution of Time-Frequency Localization Operators

Understand

We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical physics.

• These operators are fundamental to the theory of bandlimited functions and have applications in signal processing.
• Unlike previous approaches which rely on complicated formulas for the eigenvalues, our approach is simple: We build an orthonormal basis of modulated bump functions (known as wave packets in time-frequency analysis) which approximately diagonalizes the operator of interest.