The purpose of this study is to provide a comparison between the widely applied Fourier Power Spectrum (FPS) measure and the Wavelet counterpart (WT) in applications related to continuous EEG/ MEG signal analysis tasks. Both power spectrum measures are used as EEG signal features capable of characterizing and differentiating four discrete tasks in terms of cognitive complexity. This study is no...

the objective of this study is development of driver’s sleepiness using visually evoked potentials (vep). vep computed from eeg signals from the visual cortex. we use the steady state veps (ssveps) that are one of the most important eeg signals used in human computer interface systems. ssvep is a response to visual stimuli presented. we present a classification method to discriminate between cl...

BACKGROUND AND PURPOSE Cerebral embolism has been implicated in the development of cognitive and neurological deficits following bypass surgery. This study proposes methodology for estimating cerebral air embolus volume using transcranial Doppler sonography. METHODS Transcranial Doppler audio signals of air bubbles in the middle cerebral artery obtained from in vivo experiments were subjected...

The interpretation of Fourier spectra in the time domain is critically examined. Power density spectra defined and calculated in the time domain are compared with Fourier spectra in the frequency domain for three different types of variability: periodic signals, Markov processes and random shots. The power density spectra for a sample of neutron stars and black hole binaries are analyzed in bot...

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fra...

A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourie...

Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order counterparts of the power spectrum, are usually considered to characterize statistical information contained in the fields. However, it is not trivial how the Four...

A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of FFTs, which is controlled by the order N of the expansion and by the dimension D of the system. In three dimensions, for the practical value N = 3, the number of FFTs required is 20. We...

The current status of the application of the fast Fourier transform (FFT) for the auditory evoked response was summarised under for items of importance to the auditory brain stem response (ABR) as follows. (1) Digital filter: The most common way to use FFT, which facilitates quick isolation of fast and slow components from data of the same ABR wave. In addition, the proper setting of digital fi...

nowadays, radar systems have many applications and radar imaging is one of the most important of these applications. inverse synthetic aperture radar (isar) is used to form an image from moving targets. conventional methods use fourier transform to retrieve doppler information. however, because of maneuvering of the target, the doppler spectrum becomes time-varying and the image is blurred. joi...