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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 ]
For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 21 random samples (a little over two million), etc ...
Following is a partial list of spectral density estimation techniques: Non-parametric methods for which the signal samples can be unevenly spaced in time (records can be incomplete) Least-squares spectral analysis, based on least squares fitting to known frequencies; Lomb–Scargle periodogram, an approximation of the Least-squares spectral ...
Spectrum analysis can be used at audio frequencies to analyse the harmonics of an audio signal. A typical application is to measure the distortion of a nominally sinewave signal; a very-low-distortion sinewave is used as the input to equipment under test, and a spectrum analyser can examine the output, which will have added distortion products ...
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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 ]
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Let X be a Banach space, B(X) the family of bounded operators on X, and T ∈ B(X).By definition, a complex number λ is in the spectrum of T, denoted σ(T), if T − λ does not have an inverse in B(X).