Open AccessAchievable simultaneous time and frequency domain energy concentration for finite length sequences
Author(s) -
Singh Neha,
Pradhan Pyari Mohan
Publication year - 2019
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2019.0025
Subject(s) - energy (signal processing) , sequence (biology) , mathematics , upper and lower bounds , frequency domain , window function , interval (graph theory) , topology (electrical circuits) , time domain , control theory (sociology) , algorithm , mathematical optimization , mathematical analysis , computer science , spectral density , combinatorics , statistics , genetics , control (management) , artificial intelligence , computer vision , biology
For numerous applications in the field of signal processing, it is desired to design a compact window that can simultaneously concentrate maximum energy in finite time interval and frequency band. Although zero‐order discrete prolate spheroidal sequence (DPSS) meets this requirement, it is of infinite support. Limiting this sequence to finite support no longer guarantees the optimality property. This study aims at designing a discrete finite length window that can maximise the energy simultaneously in narrow time interval and frequency band. A multi‐objective optimisation approach is adopted to obtain the upper bound of maximum achievable time and frequency domain energy concentrations for finite length sequences. The optimal sequence thus obtained is termed as the optimal window with finite support (OWFS), and its various associated properties are discussed. It is shown analytically that as the support of OWFS approaches infinity, it converges to zero‐order DPSS. In order to illustrate its optimality, the compactness of the proposed OWFS is compared with those of various window functions. Extending the proposed OWFS, this study also discusses the formulation and associated properties of the zero‐order periodic DPSS. Further, the closed form expression for the upper bound of achievable time and frequency domain energy concentrations is also derived.