Recently the author has given two modifications of a nonlinear extrapolation method due to Levin and Sidi, which enable one to accurately and economically compute certain infinite integrals whose integrands have a simple oscillatory behavior at infinity. In this work these modifications are extended to cover the case of very oscillatory infinite integrals whose integrands have a complicated and...

We investigated commonly used methods (Autocorrelation, Enright, and Discrete Fourier Transform) to estimate the periodicity of oscillatory data and determine which method most accurately estimated periods while being least vulnerable to the presence of noise. Both simulated and experimental data were used in the analysis performed. We determined the significance of calculated periods by applyi...

In highly oscillatory integrals, the integrand fw(x) oscillates rapidly with a frequency ω. For very high values of ω, numerical evaluation of such integrals by Gaussian quadrature rules can be of very low accuracy. In such problems which have many applications in mathematical physics, it is important to devise algorithms with errors which decrease as fast as w−N , for some N > 0. In this paper...

purpose: to study recordings of oscillatory potentials (ops) of the electroretinogram (erg) in diabetic eyes that have no visible fundus alterations, to ascertain whether changes in sensitivity are evident when compared with recordings from age-matched controls. methods: ops of the erg were measured from 68 eyes of 34 patients with diabetes without retinopathy and from 30 eyes of 15 normal subj...

Neuronal population oscillations at a variety of frequencies can be readily seen in electroencephalographic (EEG) as well as local field potential recordings in many different species. Although these brain rhythms have been studied for many years, the methods for identifying discrete oscillatory epochs are still widely variable across studies. The "better oscillation detection" (BOSC) method ap...

K-complex is an underlying pattern in the sleep EEG. Due to the role of sleep studies inneurophysiologic and cognitive disorders diagnosis, reliable methods for analysis and detection of this patternare of great importance. In our previous work, Synchrosqueezing Transform (SST) was proposed for analysisof this pattern. SST is an EMD-like tool, which benefits from wavelet transform and reallocat...