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The spectral test is a statistical test for the quality of a class of pseudorandom number generators (PRNGs), the linear congruential generators (LCGs). [1] LCGs have a property that when plotted in 2 or more dimensions, lines or hyperplanes will form, on which all possible outputs can be found. [ 2 ]
The spectral test, which is a simple test of an LCG's quality, measures this spacing and allows a good multiplier to be chosen. The plane spacing depends both on the modulus and the multiplier. A large enough modulus can reduce this distance below the resolution of double precision numbers.
Spectral methods and finite-element methods are closely related and built on the same ideas; the main difference between them is that spectral methods use basis functions that are generally nonzero over the whole domain, while finite element methods use basis functions that are nonzero only on small subdomains (compact support).
The CLCG provides an efficient way to calculate pseudo-random numbers. The LCG algorithm is computationally inexpensive to use. [3] The results of multiple LCG algorithms are combined through the CLCG algorithm to create pseudo-random numbers with a longer period than is achievable with the LCG method by itself. [3]
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis. [ 1 ] [ 2 ] Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in the long and gapped records; LSSA mitigates such problems. [ 3 ]
Spectral analysis or spectrum analysis is analysis in terms of a spectrum of frequencies or related quantities such as energies, eigenvalues, etc. In specific areas it may refer to: Spectroscopy in chemistry and physics, a method of analyzing the properties of matter from their electromagnetic interactions
The Lehmer random number generator [1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
The multitaper method overcomes some of the limitations of non-parametric Fourier analysis.When applying the Fourier transform to extract spectral information from a signal, we assume that each Fourier coefficient is a reliable representation of the amplitude and relative phase of the corresponding component frequency.