Jitter extraction in a noisy signal by fast Fourier transform and time lag correlation

Jitter in an electronic signal is any deviation in, or displacement of, the signal in time. This paper investigates on decomposition of two types of jitter, namely, periodic and random jitter in noisy signals. Generally, an oscilloscope generates an eye diagram by overlaying sweeps of different segments of a long data stream driven by the reference clock signal. We use the fast Fourier transform with time lag correlation of the signal since we do not have a clock reference signal and apply this technique to simulated noisy signals. We separately injected a random jitter (of known amount), periodic jitter (with known frequency and amount), and both together to various modulation frequencies of sinusoidal signals. The approach is validated by several experiments with numerous values in jitter parameters. When we separately inject random jitter (5 ps) and periodic jitter (5 ps at 4.37 MHz) to the signal, we obtained the results (4.52±0.25 ps) and (4.93±0.04 ps at 4.40±0.04 MHz), respectively

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Model-based asymptotically optimal dispersion measure correction for pulsar timing

In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion measure. To correct for such variations, we develop a statistical method inspired by the maximum likelihood estimator and optimal filtering. Our method consists of two major steps. First, the spectral index and amplitude of dispersion measure variations are measured via a time-domain spectral analysis. Second, the linear optimal filter is constructed based on the model parameters found in the first step, and is used to extract the dispersion measure variation waveforms. Compared to current existing methods, this method has better time resolution for the study of short timescale dispersion variations, and generally produces smaller errors in waveform estimations. This method can process irregularly sampled data without any interpolation because of its time-domain nature. Furthermore, it offers the possibility to interpolate or extrapolate the waveform estimation to regions where no data is available. Examples using simulated data sets are included for demonstration.Comment: 15 pages, 15 figures, submitted 15th Sept. 2013, accepted 2nd April 2014 by MNRAS. MNRAS, 201

Spectral proper orthogonal decomposition

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods fail when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these "rigid" approaches, we propose a new method termed Spectral Proper Orthogonal Decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical system theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap, and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range

Ultra-violet footpoints as tracers of coronal magnetic connectivity and restructuring during a solar flare

<p><b>Context:</b> The bright, compact ultraviolet sources that appear in flare ribbons are interpreted as sites of energisation of the chromosphere, most likely by electron beams from the corona. Previously we have developed an algorithm to track these compact sources in observations by the Transition Region and Coronal Explorer (TRACE), recording position and intensity. We now exploit this further.</p> <p><b>Aims:</b> We aim at identifying conjugate footpoint pairs by cross-correlating the TRACE 1600 Å lightcurves in one particular event – the 2002-July-17 M 8.5 flare. We also seek the spatial relationship between the magnetic flux transfer (reconnection) rate, well-connected locations, and energy input by electrons.</p> <p><b>Methods:</b> We performed wavelet à trous filtering on the UV light curves, followed by a linear cross-correlation, to identify well-correlated pairs. We used RHESSI data to determine the locations of strong electron beam input.</p> <p><b>Results:</b> Maps of footpoint pairs were produced in which we can identify well-separated locations that have well-correlated 1600 Å light curves. The time lag between credible conjugate footpoint brightenings can be a few seconds. The flare magnetic connectivity is found to evolve with time. RHESSI hard X-ray sources are found where the flux transfer rate is highest.</p> <p><b>Conclusions:</b> We propose that the correlated footpoints are in fact conjugate pairs that are magnetically linked. In some instances, this linkage may be via a coronal null. The time lag in many cases is consistent with excitation by relativistic particles, but correlations with a longer time lag may suggest excitation by waves.</p&gt

Exploring the inner region of Type 1 AGNs with the Keck interferometer

The exploration of extragalactic objects with long-baseline interferometers in the near-infrared has been very limited. Here we report successful observations with the Keck interferometer at K-band (2.2 um) for four Type 1 AGNs, namely NGC4151, Mrk231, NGC4051, and the QSO IRAS13349+2438 at z=0.108. For the latter three objects, these are the first long-baseline interferometric measurements in the infrared. We detect high visibilities (V^2 ~ 0.8-0.9) for all the four objects, including NGC4151 for which we confirm the high V^2 level measured by Swain et al.(2003). We marginally detect a decrease of V^2 with increasing baseline lengths for NGC4151, although over a very limited range, where the decrease and absolute V^2 are well fitted with a ring model of radius 0.45+/-0.04 mas (0.039+/-0.003 pc). Strikingly, this matches independent radius measurements from optical--infrared reverberations that are thought to be probing the dust sublimation radius. We also show that the effective radius of the other objects, obtained from the same ring model, is either roughly equal to or slightly larger than the reverberation radius as a function of AGN luminosity. This suggests that we are indeed partially resolving the dust sublimation region. The ratio of the effective ring radius to the reverberation radius might also give us an approximate probe for the radial structure of the inner accreting material in each object. This should be scrutinized with further observations.Comment: accepted for publication in A&A Letter

Spike detection using the continuous wavelet transform

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution