The discrete Fourier transform of signals constructed through multiplicative and additive iterative procedures is determined and its specific features are considered. It is shown that – in spite of the rather different structure of multiplicative and additive signals – the Fourier transforms of both types of signals exhibit the property of self-affinity. The power spectra of additive signals pr...

Window functions are used in the estimation of power spectra, [1] and bispectra [2] in order to ensure the consistency of the periodogram and the Fourier type bispectrum estimation methods. In this paper, a three dimensional optimum bias lag window function is introduced in the estimation of the fourth order cumulant spectrum, also called trispectrum, which is estimated from the three dimesiona...

The two preceding articles developed the application of Bayesian probability theory to the problems of parameter estimation, signal detection, and model selection on quadrature NMR data in some generality. Here those procedures are used to analyze free induction decay data, when the models are sinusoidal. The exact relationship between Bayesian probability theory and the discrete Fourier-transf...

The scaling exponent of a 1/ f noise time series is commonly estimated from the power-law slope of its Fourier power spectrum. Here I show that because 1/ f noises typically have significant power above the Nyquist frequency, measurements of their power spectra will often be severely distorted by aliasing, not only near the Nyquist frequency, but also far below it. I show that spectral aliasing...

background: driver fatigue is one of the major implications in transportation safety and accounted for up to 40% of road accidents. this study aimed to analyze the eeg alpha power changes in partially sleep-deprived drivers while performing a simulated driving task. methods: twelve healthy male car drivers participated in an overnight study. continuous eeg and eog records were taken during driv...

This dissertation introduces a theoretical framework to study different sampling patterns in the spherical domain and their effects in the evaluation of global illumination integrals. Evaluating illumination (light transport) is one of the most essential aspect in image synthesis to achieve realism which involves solving multi-dimensional space integrals. Monte Carlo based numerical integration...

Typically, image motion analysis in the frequency domain is performed according to the Motion From Fourier Coeecients, or MFFC principle. However , this principle excludes a class of motion that does not generate power spectra containing the origin of the frequency domain, which is usually referred to as Non-Fourier motion. This type of motion includes phenomena relevant to motion analysis such...

Recent Fourier analyses of fossil extinction data have indicated that the power spectrum of extinction during the Phanerozoic may take the form of 1/f noise, a result which, it has been suggested, could be indicative of the presence of “critical dynamics” in the processes giving rise to extinction. In this paper we examine extinction power spectra in some detail, using family-level data from a ...

Detection of deep and hidden mineralization using the surface geochemical data is a challenging subject in the mineral exploration. In this work, a novel scenario based on the spectrum–area fractal analysis (SAFA) and the principal component analysis (PCA) has been applied to distinguish and delineate the blind and deep Mo anomaly in the Dalli Cu–Au porphyry mineralization area. The Dalli miner...

The Lomb-Scargle periodogram is widely used for the estimation of the power spectral density of unevenly sampled data. A small extension of the algorithm of the Lomb-Scargle periodogram permits the estimation of the phases of the spectral components. The amplitude and phase information is sufficient for the construction of a complex Fourier spectrum. The inverse Fourier transform can be applied...