Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II

1961/01/01 by H. J. Landau, H. O. Pollak · 12 citations
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Scientific Research and Discoveries #Ultrasonics and Acoustic Wave Propagation

paper · doi:10.1002/j.1538-7305.1961.tb03977.x

crossref issued 1961/01/01 · crossref published 1961/01/01 · crossref published-print 1961/01/01 · openalex publication_date 1961/01/01 · crossref published-online 2013/07/29 · crossref created 2013/07/29 · crossref deposited 2020/10/14 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31

Abstract

The theory developed in the preceding paper1is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.

Cited by

• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-III: The Dimension of the Space of Essentially Time- and Band-Limited Signals
• Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty-V: The Discrete Case
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• Angular performance measure for tighter uncertainty relations
• A Closer Look at the Uncertainty Relation of Position and Momentum
• Heisenberg’s uncertainty principle for simultaneous measurement of positive-operator-valued measures
• Collision entropy and optimal uncertainty
• Generalized Landau-Pollak uncertainty relation
• Uncertainty Principles and Signal Recovery
• Entanglement criteria via concave-function uncertainty relations
• The uncertainty principle: A mathematical survey
• Prolate spheroidal wave function [wikipedia]