A compact formulation for conditioned spectral density function analysis by means of the LDLH matrix factorization

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.

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The bootstrap applied to power spectral density function estimation

Biometrika ◽

10.1093/biomet/73.1.135 ◽

1986 ◽

Vol 73 (1) ◽

pp. 135-141 ◽

Cited By ~ 26

Author(s):

J. W. H. SWANEPOEL ◽

J. W. J. VAN WYK

Keyword(s):

Spectral Density ◽

Density Function ◽

Power Spectral Density ◽

Spectral Density Function ◽

Function Estimation ◽

Power Spectral Density Function ◽

Power Spectral ◽

Density Function Estimation

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Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function

Journal of Mechanical Design ◽

10.1115/1.4036582 ◽

2017 ◽

Vol 139 (7) ◽

Cited By ~ 16

Author(s):

Shuangcheng Yu ◽

Yichi Zhang ◽

Chen Wang ◽

Won-kyu Lee ◽

Biqin Dong ◽

...

Keyword(s):

Spectral Density ◽

Density Function ◽

Design Methodology ◽

Light Trapping ◽

Spectral Density Function ◽

Particle Type ◽

Bottom Up ◽

Design Representation ◽

Material Systems ◽

Channel Type

Quasi-random nanostructures are playing an increasingly important role in developing advanced material systems with various functionalities. Current development of functional quasi-random nanostructured material systems (NMSs) mainly follows a sequential strategy without considering the fabrication conditions in nanostructure optimization, which limits the feasibility of the optimized design for large-scale, parallel nanomanufacturing using bottom-up processes. We propose a novel design methodology for designing isotropic quasi-random NMSs that employs spectral density function (SDF) to concurrently optimize the nanostructure and design the corresponding nanomanufacturing conditions of a bottom-up process. Alternative to the well-known correlation functions for characterizing the structural correlation of NMSs, the SDF provides a convenient and informative design representation that maps processing–structure relation to enable fast explorations of optimal fabricable nanostructures and to exploit the stochastic nature of manufacturing processes. In this paper, we first introduce the SDF as a nondeterministic design representation for quasi-random NMSs, as an alternative to the two-point correlation function. Efficient reconstruction methods for quasi-random NMSs are developed for handling different morphologies, such as the channel-type and particle-type, in simulation-based microstructural design. The SDF-based computational design methodology is illustrated by the optimization of quasi-random light-trapping nanostructures in thin-film solar cells for both channel-type and particle-type NMSs. Finally, the concurrent design strategy is employed to optimize the quasi-random light-trapping structure manufactured via scalable wrinkle nanolithography process.

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