Autocorrelation Procedure Research Articles

Time series clustering using fragmented autocorrelations

We propose and study an autocorrelation procedure designed to characterize and compare large sets of long time series. This time-domain procedure is contrasted with a frequency-domain approach that has recently been introduced and discussed in the literature. In both cases, instead of using all the information available from data, which would be computationally very expensive, adequate regularization rules select and summarize the most relevant information suitable for clustering purposes. Essentially, we suggest to use the autocorrelation coefficients of the time series that are only computed around the lags of greatest interest. Then, we study this method in several ways. We argue theoretically that fragmenting the autocorrelation function can have efficiency advantages when comparing time series. By means of a large simulation study, we show that the suggested procedure can condense the relevant information of the time series. We compare its results with those from the frequency domain counterpart. We further illustrate this procedure in a study of the evolution of several stock markets indices and show the effect of recent financial crises on the behaviour of these indices.

Efficient method for the field‐programmable gate arrays calculation of Wigner‐Ville distribution

Various signals of finite length are often analysed by the Wigner-Ville distribution (WVD). Thus, this article deals with the implementation of their discrete WVDs on field-programmable gate arrays (FPGAs). For the discrete WVD, its calculation procedures are composed of the autocorrelation function and Fourier transform. Since the autocorrelation procedure is the most time-consuming step in the entire computation process, the authors analyse the calculation procedure of autocorrelation function in detail. Here the proposed efficient method just calculates partial non-zero elements of the autocorrelation matrices in order to reduce the computation complexity. The FFT (built-in FPGAs) is then utilised to acquire the discrete WVD. In addition, the idea of the fully-pipelined and parallelism is borrowed to reduce the running time but at the cost of recourses. Finally, the authors provide implementations of both authors proposed method and two other algorithms on different FPGAs. The experimental results show that the Intel Arria-10 FPGA families are the better choice in the floating point arithmetic and that authors method has the best performance.

A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades

Abstract We study intensity variations, as measured by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, in a solar coronal arcade using a newly developed analysis procedure that employs spatio-temporal autocorrelations. We test our new procedure by studying large-amplitude oscillations excited by nearby flaring activity within a complex arcade and detect a dominant periodicity of 12.31 minutes. We compute this period in two ways: from the traditional time–distance fitting method and using our new autocorrelation procedure. The two analyses yield consistent results. The autocorrelation procedure is then implemented on time series for which the traditional method would fail due to the complexity of overlapping loops and a poor contrast between the loops and the background. Using this new procedure, we discover the presence of small-amplitude oscillations within the same arcade with 9.13 and 9.81 minute periods prior and subsequent to the large-amplitude oscillations, respectively. Consequently, we identify these as “decayless” oscillations that have only been previously observed in nonflaring loop systems.

Two-year changes in gait variability in community-living older adults

BackgroundIncreases in stride-to-stride fluctuations (gait variability) are common among older adults, but little is known about the natural progression of gait variability with increasing age. Research questionDoes gait variability change with increasing age in a group of community-living older adults? MethodsThe participants were community-living volunteers between 70–81 years, who were tested with a two-year interval between tests. They walked 6.5 m under four different conditions: At preferred speed, at fast speed, during a dual task condition and on an uneven surface. Trunk accelerations in the anteroposterior (AP), mediolateral (ML) and vertical (V) direction were captured using a body-worn sensor worn at the lower back. Gait variability was estimated using an autocorrelation procedure, where coefficients tending towards 1.0 indicated low variability and 0.0 as high variability. To estimate change, we used an ANOVA-procedure with baseline gait speed as a covariate. ResultsAt baseline, 85 older adults were tested, and data for 56 of these were available for analysis over a two-year period of time. The average age at inclusion was 75.8 years (SD 3.43) and 60% were women. During preferred speed walking, variability increased in the AP direction (mean difference 0.05, p = .038), during fast speed walking it increased in the V direction (mean difference 0.04, p = .037) and during dual task-walking, it increased in the ML and V directions (mean differences 0.03, p = .032 and 0.09, p = .020 respectively). SignificanceThe findings from this study could be helpful for discriminating between normal and pathological progression of gait variability in older adults.

Fluorescence lifetime estimation by 1-bit photon autocorrelation procedure from time-series data recorded using a high-speed digitizer

We propose a photon-counting fluorescence lifetime measurement scheme that uses a 1-bit autocorrelation procedure. The proposed scheme is an extension of the previously reported lifetime measurements using the autocorrelation analysis (Nishimura et al. in: Phys Med Biol 48:N283–N290, 2003; Nishimura et al. in: J Biomed Opt 12:020503, 2007). The fluorescence photons obtained from a high-repetition-rate, pulsed excitation light source are fed into a photodetector, and its output photoelectron pulse train is stored in a transient memory composed of a high-speed digitizer that retains time information over a large number of excitation cycles. After the stored data have been binarized, a 1-bit autocorrelation procedure is performed to estimate the fluorescence lifetimes through a repetitive curve-fitting process. We could successfully demonstrate this scheme in nanosecond fluorescence lifetime measurements with a progressed high-speed digitizer, which requires no synchronization with the excitation timing. To date, the minimum sampling interval and the maximum number of sample points of the digitizer are 400 ps and ~ 1 × 109, respectively. We present the results of some fluorescence lifetime measurements of standard samples that were performed as a proof of principle experiment.

Crustal structure beneath Tierra del Fuego, Argentina, inferred from seismic P-wave receiver functions and ambient noise autocorrelations

We investigate the structure of the crust beneath the main island of Tierra del Fuego through a teleseismic receiver function analysis and ambient seismic noise autocorrelation using data of four available broad-band stations. The area is situated in a remote region of southern Argentina where the interaction between the South American and Scotia plates define the Magallanes-Fagnano Fault System. Crustal thickness, Vp/Vs ratios and S-wave velocity models were estimated using the H-k stacking method and the inversion of receiver functions with the Neighbourhood Algorithm. Furthermore, we applied an ambient seismic noise autocorrelation procedure to identify PmP Moho reflections at all stations. The three methods provide consistent estimates for the crustal thickness which ranges from about 24.5 km in the northern part of the Island to about 39.2 km in the south. The lowest and highest values of S-wave velocity found, in the most superficial layers of the crust, correlate with the presence of Tertiary and upper Cretacic sediments in the north and with older geological units composed by more consolidated lithologies in the south, respectively. Despite the diverse geological and tectonic settings present, our results do not change significantly for different parameters or subsidiary data sets, i.e., showing the robustness of our models which likely represent closely the local structure beneath the Island. This area is considered a very seismically active one and its crustal structure has been little explored demonstrating the importance of having new models and the necessity to increase the station coverage to allow a more detailed study of the region. Furthermore, the models presented here provide better constraints on the crustal structure, and will facilitate studies of the regional seismicity that can improve our understanding of the seismic hazard posed by earthquakes such as the magnitude 7.5 and 7.8 events that occurred in 1949.

Accelerometer-Based Step Regularity Is Lower in Older Adults with Bilateral Knee Osteoarthritis.

Purpose: To compare the regularity and symmetry of gait between a cohort of older adults with bilateral knee osteoarthritis (OA) and an age and sex-matched control group of older adults with healthy knees.Methods: Fifteen (8 females) older adults with knee OA (64.7 ± 6.7 years) and fifteen (8 females) pain-free controls (66.1 ± 10.0 years) completed a 9-min. walk at a self-selected, comfortable speed while wearing a single waist-mounted tri-axial accelerometer. The following gait parameters were compared between the two groups according to sex: mean step time, mean stride time, stride and step regularity (defined as the consistency of the stride-to-stride or step-to-step pattern) and the symmetry of gait (defined as the difference between step and stride regularity) as determined by an unbiased autocorrelation procedure that analyzed the pattern of acceleration in the vertical, mediolateral and anteroposterior directions.Results: Older adults with knee OA displayed significantly less step regularity in the vertical (p < 0.05) and anteroposterior (p < 0.05) directions than controls. Females with knee OA were also found to have significantly less mediolateral step regularity than female controls (p < 0.05), whereas no difference was found between males.Conclusion: The results showed that the regularity of the step pattern in individuals with bilateral knee OA was less consistent compared to similarly-aged older adults with healthy knees. The findings suggest that future studies should investigate the relationship between step regularity, sex and movement direction as well as the application of these methods to the clinical assessment of knee OA.

Development of cross-correlation spectrometry and the coherent structures of maser sources

Abstract We have developed a new method of data processing for radio telescope observation data to measure time-dependent temporal coherence, and we have named it “cross-correlation spectrometry” (XCS). XCS is an autocorrelation procedure that expands time lags over the integration time and is applied to data obtained from a single-dish observation. The temporal coherence property of received signals is enhanced by XCS. We tested the XCS technique using the data of strong H2O masers in W 3 (H2O), W 49 N, and W 75 N. We obtained the temporal coherent lengths of the maser emission to be 17.95 ± 0.33 μs, 26.89 ± 0.49 μs, and 15.95 ± 0.46 μs for W 3 (H2O), W 49 N, and W 75 N, respectively. These results may indicate the existence of a coherent astrophysical maser.

Wireless Tri-Axial Trunk Accelerometry Detects Deviations in Dynamic Center of Mass Motion Due to Running-Induced Fatigue.

Small wireless trunk accelerometers have become a popular approach to unobtrusively quantify human locomotion and provide insights into both gait rehabilitation and sports performance. However, limited evidence exists as to which trunk accelerometry measures are suitable for the purpose of detecting movement compensations while running, and specifically in response to fatigue. The aim of this study was therefore to detect deviations in the dynamic center of mass (CoM) motion due to running-induced fatigue using tri-axial trunk accelerometry. Twenty runners aged 18–25 years completed an indoor treadmill running protocol to volitional exhaustion at speeds equivalent to their 3.2 km time trial performance. The following dependent measures were extracted from tri-axial trunk accelerations of 20 running steps before and after the treadmill fatigue protocol: the tri-axial ratio of acceleration root mean square (RMS) to the resultant vector RMS, step and stride regularity (autocorrelation procedure), and sample entropy. Running-induced fatigue increased mediolateral and anteroposterior ratios of acceleration RMS (p < .05), decreased the anteroposterior step regularity (p < .05), and increased the anteroposterior sample entropy (p < .05) of trunk accelerometry patterns. Our findings indicate that treadmill running-induced fatigue might reveal itself in a greater contribution of variability in horizontal plane trunk accelerations, with anteroposterior trunk accelerations that are less regular from step-to-step and are less predictable. It appears that trunk accelerometry parameters can be used to detect deviations in dynamic CoM motion induced by treadmill running fatigue, yet it is unknown how robust or generalizable these parameters are to outdoor running environments.

Direct Measurement of the Magnetic Cluster Size Using High-Resolution Magnetic Force Microscopy

High-resolution magnetic force microscopy was used to image high linear density tracks and measure the magnetic cluster size of the ac-erased state of perpendicular magnetic recording media. The full-width at half-maximum (FWHM) of the auto-correlation function corresponding to an ac-erased region determines the correlation length, i.e., the magnetic cluster size. This is demonstrated by comparing the calculated FWHM of auto-correlation function obtained on simulated Voronoi granular structures with the expected value for magnetically decoupled grains. The cluster size we obtained using the auto-correlation procedure is about four grain sizes. The impact of the finite cluster size on the recording performance was assessed by following the trend of tracks' auto-correlation function with increasing the linear density.

A modelling approach to infer the effects of wind farms on landscape connectivity for bats

Little is known about the potentially disrupting effects of wind farms on the habitat connectivity of flying vertebrates at the landscape scale. We developed a regional-scale model to assess the wind farm impact on bat migration and commuting routes. The model was implemented for the bat Nyctalus leisleri in a region of central Italy currently undergoing considerable wind farm development. A Species Distribution Model (SDM) for N. leisleri was generated using the MaxEnt algorithm based on 47 presence records (reduced to 19 after the autocorrelation procedure) and 10 environmental variables derived from topographic and land cover maps. We used the SDM to create a map of connectivity using the software UNICOR to identify potential commuting corridors (PCCs). The incidence of each wind farm on bat flight corridors was assessed by overlaying the existing (380) and planned (195) turbine locations onto the PCCs. The SDM was statistically robust (AUC > 0.8). Most of the corridors were concentrated in the western part of the region, which hosts the largest suitable areas for the species; most of the existing (54 %) and planned (72 %) wind farms interfered with important corridors connecting the western and the eastern parts of the region. Our results provide key information on the impact of the wind farm industry on biodiversity on a regional scale. The novel approach adopted, based on SDM and connectivity analysis, could be easily extended to other flying vertebrates and landscapes and constitutes a promising planning tool necessary for harmonizing the development of renewable energy infrastructures with issues of biodiversity conservation.

Evaluation of age-related differences in the stride-to-stride fluctuations, regularity and symmetry of gait using a waist-mounted tri-axial accelerometer

PurposeTo compare the stride-to-stride fluctuations, regularity and symmetry of gait using a body-fixed accelerometer in a group of healthy young and healthy older adults. MethodsForty-one healthy young adults (24±3 years) and forty-one healthy older adults (76±5 years) completed a 10-min walk at a self-selected, normal walking speed while wearing a single waist-mounted tri-axial accelerometer. The following gait parameters were compared between age groups: mean step and stride time, step and stride time variability, stride time fractal scaling index and the regularity and symmetry of the acceleration pattern in the vertical, mediolateral and anteroposterior directions (unbiased autocorrelation procedure). ResultsOlder adults displayed significantly greater step and stride time variability (p<0.05) and a lower stride time fractal scaling index (p<0.01), as well as significantly less regularity (p<0.05) and symmetry (p<0.05) of the anteroposterior accelerations. ConclusionThe results show that healthy older adults possess greater temporal gait variability, as well as a less-organized and repeatable pattern of variability and acceleration in the direction of motion, than younger adults. The findings also suggest the presence of an age-related decline in the anteroposterior control of gait, but not in the vertical and mediolateral control of gait.

A two-stage autocorrelation method for frequency estimation of sinusoidal signal

A two-stage autocorrelation method is proposed for frequency estimation of a complex sinusoidal signal in complex additive white Gaussian noise. In the first stage, a function about signal frequency is constructed via an autocorrelation procedure. By the Least-Square (LS) principle, the signal frequency is estimated from the function. In the second stage, the estimated error of signal frequency in the first stage is defined. Applying the Taylor series, a function about the estimated error of signal frequency is conducted from the autocorrelation function. Applying the LS estimation once more, the estimate of estimated error of frequency in the first stage is obtained. Then the fine estimate of signal frequency is obtained. Simulation results show that the performance of proposed method can approach the Cramer–Rao lower bound in the whole frequency range.

Crustal properties from seismic station autocorrelograms

S U M M A R Y Stations on the Australian continent receive a rich mixture of continuous ground motion with ambient seismic noise from the surrounding oceans, and numerous small earthquakes in the earthquake belts to the north in Indonesia, and east in Tonga-Kermadec, as well as more distant source zones. The ground motion at a seismic station contains information about the structure in the vicinity of the site, and this can be exploited by applying an autocorrelation procedure to the continuous records. By creating stacked autocorrelograms of the ground motion at a single station, information on crust properties can be extracted in the form of a signal that includes the crustal reflection response convolved with the autocorrelation of the combined effect of source excitation and the instrument response. After applying suitable high-pass filtering, the reflection component can be extracted to reveal the most prominent reflectors in the lower crust, which often correspond to the reflection at the Moho. Because the reflection signal is stacked from arrivals from a wide range of slownesses, the reflection response is somewhat diffuse, but still sufficient to provide useful constraints on the local crust beneath a seismic station. Continuous vertical component records from 223 stations (permanent and temporary) across the continent have been processed using autocorrelograms of running windows 6 hr long with subsequent stacking.A distinctive pulsewith a time offset between 8 and 30 s fromzero is found in the autocorrelation results, with frequency content between 1.5 and 4 Hz, suggestingP-wave multiples trapped in the crust. Synthetic modelling, with control of multiple phases, shows that a local pmp phase can be recovered with the autocorrelation approach. This identification enables us to make out the depth to the most prominent crustal reflector across the continent. We obtain results that largely conform to those from previous studies using a combination of data from refraction, reflection profiles and receiver functions. This approach can be used for crustal property extraction using just vertical component records, and effective results can be obtained with temporary deployments of just a few months.

Analysis of gait and balance through a single triaxial accelerometer in presymptomatic and symptomatic Huntington's disease

PurposeTo investigate the capacity of a single triaxial accelerometer sensor in detecting gait and balance impairments in pre-manifest and manifest Huntington's disease (HD) subjects. MethodsFourteen manifest HD (MHD) (age: 51.83±14.8), ten pre-manifest HD (PHD) (age: 44.8±11.7) and ten healthy subjects (HLY) (age: 56.4±10.9) were recruited. The sensor was attached to the upper sternum as subjects completed gait and Romberg balance tests. An inverted pendulum model of the body's centre of mass and an unbiased autocorrelation procedure were employed to derive gait parameters from the triaxial accelerometer signal. The accuracy of the gait measurements was compared to those recorded by a computerized walkway. ResultsStrong agreement was seen between the sensor and the walkway; cadence (ICC=0.95, CI=[0.75, 0.97]), velocity (ICC=0.94, CI=[0.75, 0.97]) and step length (ICC=0.89, CI=[0.77, 0.95]). Sensor derived velocity was significantly higher in HLY (p<0.001) and PHD (p<0.005) when compared to MHD. Step and stride length was significantly longer in HLY (p<0.05) and PHD (p<0.001) when compared to MHD. Significant differences between subject groups across all four balance tasks (p<0.001) were found. ConclusionAn accelerometer based sensor may be an effective means of differentiating between pre-manifest and manifest Huntington's disease subjects.

Real-Time Gait Cycle Parameter Recognition Using a Wearable Accelerometry System

This paper presents the development of a wearable accelerometry system for real-time gait cycle parameter recognition. Using a tri-axial accelerometer, the wearable motion detector is a single waist-mounted device to measure trunk accelerations during walking. Several gait cycle parameters, including cadence, step regularity, stride regularity and step symmetry can be estimated in real-time by using autocorrelation procedure. For validation purposes, five Parkinson’s disease (PD) patients and five young healthy adults were recruited in an experiment. The gait cycle parameters among the two subject groups of different mobility can be quantified and distinguished by the system. Practical considerations and limitations for implementing the autocorrelation procedure in such a real-time system are also discussed. This study can be extended to the future attempts in real-time detection of disabling gaits, such as festinating or freezing of gait in PD patients. Ambulatory rehabilitation, gait assessment and personal telecare for people with gait disorders are also possible applications.

Two-stage autocorrelation approach for accurate single sinusoidal frequency estimation

A two-stage autocorrelation approach is proposed for single-tone frequency estimation of a real sinusoid in white noise. In the first stage, we transform the received data to another noisy sinusoidal sequence of same frequency via an autocorrelation procedure. Autocorrelation functions of the converted sequence are then employed for frequency estimation in the second stage. A simple frequency estimator is first derived, followed by a generalized algorithm. Computer simulations are included to illustrate the accuracy of our proposed approach via comparison with Cramér–Rao lower bound and several conventional frequency estimators.

Synchrony in a Wild Turkey Population and its Relationship to Spring Weather

Abstract: Synchrony is an important component of wildlife population dynamics because it describes spatial pattern in temporal population fluctuations. The strength and spatial extent of synchrony can provide information about the extrinsic and intrinsic forces that shape population structure. Wild turkey (Meleagris gallopavo silvestris) populations undergo annual fluctuations, possibly due to variation in weather during the reproductive season. To determine if spring weather plays a role in synchronizing wild turkey populations, we used a modified Mantel‐type spatial autocorrelation procedure to measure the synchrony in fall wild turkey harvest data collected in 443 townships from 1990 to 1995 and compared this to the pattern of synchrony in spring weather variables (May rainfall and temp) over the same period. We measured correlation using Spearman correlation coefficients between the total fall harvests from 1990 to 1995 for each pair of townships, and sorted pairs into 6 50‐km distance intervals. We calculated a mean correlation coefficient for each interval and estimated its P‐value using resampling. We found moderately significant synchrony in the fall harvest (rs = 0.12‐0.34, P &lt; 0.008) among township pairs &lt;150 km apart, but no significant synchrony beyond this distance. In contrast, both May temperature (r = 0.82‐0.90, P &lt; 0.001) and rainfall (r = 0.49‐0.76, P &lt; 0.001) were strongly synchronized across all 6 distance intervals. Visual inspection of time series in the wild turkey fall harvest suggests that populations may be synchronized in some years when weather promotes high reproductive success (i.e., a synchronized growth peak) and asynchronous in other years. Knowledge of the spatial dynamics of wild turkey populations will aid wildlife managers in estimating population change, setting harvest quotas, and managing habitat.

Improvement of frequency extraction accuracy of linear predictive analysis by a combination of autocorrelation and integral procedure for noise wave shape

AbstractThe accurate and rapid identification or detection of the electrical noise sources causing noise malfunctions in communication equipment is an important issue in determining corrective measures. In this paper, we explain an improvement in the frequency extraction accuracy of linear predictive analysis for noise waveforms in order to identify the noise sources from noise waveforms such as the audible noise generated by communication equipment like telephones and noise currents penetrating into the communication equipment. In this study, we propose an improvement of the frequency extraction accuracy of linear predictive analysis by using correlation and integration. This method preserves specific frequency components of the original noise waveforms although correlation and integration are performed. In this paper, we divide the noise waveform into finite‐length segments, correlate and integrate the time series data within a given segment, and formulate dynamic frequency analysis (time–frequency analysis) based on linear predictive analysis for the time series data in the postprocessing. We also verify the effectiveness of the proposed method by using known noise waveforms. The result of applying the proposed method to a noise waveform that convolved white noise with sine wave signals having known frequencies was clearly the ability to extract the frequencies of the sine waves included in the noise waveform even for a signal‐to‐noise ratio (SNR) of 0 dB with an error range of about 10 to 15%. This assumes that the frequencies of the sine waves included in the noise can be extracted even under the worst case SNR due to the suppression of white noise by the correlation and the emphasis of the low‐frequency components by the integration. Thus, we show that the characteristic frequencies in the noise waveform can be accurately extracted by using linear predictive analysis combining correlation and integration, and present the remaining issues. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(1): 1–11, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20153

Interstride trunk acceleration variability but not step width variability can differentiate between fit and frail older adults

Variability of gait may be regarded as a sign of adaptability and thus a requirement for successful locomotion, or as a sign of impaired balance control. In this study we examined the role of step width variability (SWV) and interstride trunk acceleration variability in two groups of fit and frail old people. We investigated the association of these measures and how they differentiated the two groups. We examined 33 fit older adults (mean age 73 years, S.D. 3.3 years) and 32 frail old people (mean age 80 years, S.D. 4.0 years). Subjects performed timed walking at different speeds ranging from very slow to very fast. SWV was measured from footprints. Trunk accelerations were registered by a triaxial accelerometer and interstride trunk acceleration variability assessed by an unbiased autocorrelation procedure. All measures were normalized to a walking speed of 0.9 m/s to avoid the confounding effect of gait speed on speed dependent gait parameters. SWV demonstrated low association with the trunk variability measures, and did not differ between groups. The frail group had lower mediolateral (P=0.015), but higher vertical (P=0.015) and anteroposterior (P<0.02) trunk variability than the fit group. Trunk variability classified 80% of the subjects correctly into their respective group (sensitivity=0.75, specificity=0.85). The findings are compatible with a notion that mediolateral interstride trunk variability represents a different aspect of motor control than variability in the direction of propulsion.