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Discrete Prolate Spheroidal Sequence

Encyclopedia of Mathematical Geosciences

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

Definition

The discrete prolate spheroidal sequences (DPSSs) are maximally concentrated in both the time and frequency domains. This is a crucial property for applications in power spectrum estimation. The DPSSs comprise sets of real-valued orthonormal sequences (discrete functions) with the following properties: (i) They are limited within the spectral band [–W, W], where W > 0. (ii) The total energy of the sequence (i.e., the sum of the squares of the amplitudes) over a finite time interval is maximized. The time-limited DPSSs, also known as the Slepian sequences, are orthonormal sequences with the following properties: (i) They are time-limited within a finite time interval. (ii) They exhibit maximal spectral concentration in the frequency band [–W, W]. The DPSSs are parametrized in terms of the length N of the temporal sequence, the bandwidth W, and the order k = 0, 1, …N – 1 of the Slepian sequence.

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In Fourier analysis, it is known that functions cannot be fully localized...

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Abbreviations

DFT:

Discrete Fourier Transform

DPSS:

Discrete Prolate Spheroidal Sequence

MTM:

Multitaper Method

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Correspondence to Dionissios T. Hristopulos .

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Hristopulos, D.T. (2021). Discrete Prolate Spheroidal Sequence. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_93-1

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  • DOI: https://doi.org/10.1007/978-3-030-26050-7_93-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26050-7

  • Online ISBN: 978-3-030-26050-7

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Chapter history

  1. Latest

    Discrete Prolate Spheroidal Sequence
    Published:
    05 August 2022

    DOI: https://doi.org/10.1007/978-3-030-26050-7_93-2

  2. Original

    Discrete Prolate Spheroidal Sequence
    Published:
    28 August 2021

    DOI: https://doi.org/10.1007/978-3-030-26050-7_93-1