A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

Estimation of Time-Limited Channel Spectra From Nonuniform Samples

This paper deals with the estimation of a time-invariant channel spectrum from its own nonuniform samples, assuming there is a bound on the channel’s delay spread. Except for this last assumption, this is the basic estimation problem in systems providing channel spectral samples. However, as shown in the paper, the delay spread bound leads us to view the spectrum as a band-limited signal, rather than the Fourier transform of a tapped delay line (TDL). Using this alternative model, a linear estimator is presented that approximately minimizes the expected root-mean-square (RMS) error for a deterministic channel. Its main advantage over the TDL is that it takes into account the spectrum’s smoothness (time width), thus providing a performance improvement. The proposed estimator is compared numerically with the maximum likelihood (ML) estimator based on a TDL model in pilot-assisted channel estimation (PACE) for OFDM.

A high-resolution binocular video-oculography system: assessment of pupillary light reflex and detection of an early incomplete blink and an upward eye movement

Background: The pupillary light reflex characterizes the direct and consensual response of the eye to the perceived brightness of a stimulus. It has been used as indicator of both neurological and optic nerve pathologies. As with other eye reflexes, this reflex constitutes an almost instantaneous movement and is linked to activation of the same midbrain area. The latency of the pupillary light reflex is around 200 ms, although the literature also indicates that the fastest eye reflexes last 20 ms. Therefore, a system with sufficiently high spatial and temporal resolutions is required for accurate assessment. In this study, we analyzed the pupillary light reflex to determine whether any small discrepancy exists between the direct and consensual responses, and to ascertain whether any other eye reflex occurs before the pupillary light reflex. Methods: We constructed a binocular video-oculography system two high-speed cameras that simultaneously focused on both eyes. This was then employed to assess the direct and consensual responses of each eye using our own algorithm based on Circular Hough Transform to detect and track the pupil. Time parameters describing the pupillary light reflex were obtained from the radius time-variation. Eight healthy subjects (4 women, 4 men, aged 24–45) participated in this experiment. Results: Our system, which has a resolution of 15 microns and 4 ms, obtained time parameters describing the pupillary light reflex that were similar to those reported in previous studies, with no significant differences between direct and consensual reflexes. Moreover, it revealed an incomplete reflex blink and an upward eye movement at around 100 ms that may correspond to Bell’s phenomenon. Conclusions: Direct and consensual pupillary responses do not any significant temporal differences. The system and method described here could prove useful for further assessment of pupillary and blink reflexes. The resolution obtained revealed the existence reported here of an early incomplete blink and an upward eye movement.