Achievable simultaneous time and frequency domain energy concentration for finite length sequences. Issue 8 (1st October 2019) - Singh, Neha; Pradhan, Pyari Mohan
Abstract : 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.