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RESEARCH

Following is a list of research studies, finite element models and computational codes.

FINITE ELEMENT MODELS OF INSTRUMENTED BUILDINGS AND BRIDGES

SIX-STORY STEEL BUILDING IN BURBANK CALIFORNIA

Finite element model calibration of an instrumented six-story steel moment frame building in Burbank, California.

DOCUMENTATION OpenSEES FEM OpenSEES FEM_Pushover SAP2000 FEM ESDOF_Excel_File
SEVEN-STORY (HOLIDAY Inn) RC Building in Van Nuys California

Finite element model calibration of an instrumented seven-story reinforced concrete building in Van Nuys, California.

OpenSEES FEM SAP2000 FEM
THIRTEEN-STORY STEEL Building in Southern California

Finite element model calibration of an instrumented thirteen-story steel moment frame building in in South San Fernando Valley, California.

Documentation OpenSEES FEM SAP2000 FEM
Nineteen-Story Building in Southern California

Finite element model calibration of an instrumented nineteen-story steel moment frame building in Century City, Los Angeles, California.

OpenSEES FEM
FIFTY-TWO-STORY BUILDING IN DOWNTOWN LOS ANGELES CALIFORNIA

Finite element model calibration of an instrumented 52-story steel moment frame building in downtown Los Angeles, California.

OpenSEES FEM SAP2000 FEM
Ordinary Standard Skew Bridge in California

Finite element model of a typical skewed-bridge built in California.

Documentation OpenSEES FEM

Pushover Analysis

Adaptive Modal Combination Procedure for Nonlinear Static Analysis of Building Structures

A new pushover analysis procedure accounts for higher mode effects by combining the response of individual modal pushover analyses and incorporates the effects of varying dynamic characteristics during the inelastic response via its adaptive feature. The applied lateral forces used in the progressive pushover analysis are based on instantaneous inertia force distributions across the height of the building for each mode. A novel feature of the procedure is that the target displacement is estimated and updated dynamically during the analysis by incorporating energy-based modal capacity curves in conjunction with constant-ductility capacity spectra. Hence it eliminates the need to approximate the target displacement prior to commencing the pushover analysis.

OpenSEES FEM with MatLAB OpenSEES Source Code for Adaptive Pushover

Ground-motion Prediction

Graizer – Kalkan 2015 Ground Motion Prediction Equations for Shallow Crustal Active Tectonic Regions (Excel File)

Graizer-Kalkan (2015) ground motion prediction equation (GMPE) is designed to predict peak-ground acceleration and 5% damped pseudo-spectral acceleration response ordinates for shallow-crustal continental earthquakes to be used in earthquake-engineering applications including probabilistic and deterministic seismic hazard analyses. The link offers a simple-to-use excel file of the GK15.

GK15 GMPE Excel File
Kalkan - Gulkan Ground Motion Prediction Equations for Turkey

A ground motion prediction equations (GMPEs) for Turkey was developed by Kalkan and Gulkan (2004) using then available indigenous database constituting 112 strong ground motion records from 57 earthquakes that occurred between 1976 and 2003. This model predicts peak ground acceleration (PGA) and response spectral ordinates at 5% of critical damping in the range of 0.1 to 2.0 s (total of 46 periods) over the full range of magnitudes (M4 to 7.5) and distances (Rjb up to 250 km). This model is for the maximum horizontal component of ground motion.

KG04 GMPE MatLAB Function

Seismic Hazard Analysis

Earthquake Potential of California Considering Site Effects

National seismic hazard maps plot the peak ground acceleration (PGA) and spectral acceleration (SA) at 0.2 and 1.0 sec with 2% and 10% probability of exceedance (PE) in 50 years. These acceleration levels were computed for uniform “firm rock” site conditions (VS30 = 760 m/sec), and therefore the potential spatial variability of ground motion associated with different site conditions are not considered. In this study, we have combined the National Seismic Hazard model with the California geologic map showing 17 generalized geologic units that can be defined by their VS30. We regrouped these units into 7 VS30 values and calculated a probabilistic seismic hazard map for the entire state for each VS30 value. By merging seismic hazard maps based on the 7 different VS30 values, a suite of seismic hazard maps was computed for 0.2 and 1.0 sec spectral ordinates at 2% PE in 50 years. The improved hazards maps explicitly incorporate the site effects and their spatial variability on ground motion estimates.

DOCUMENTATION
Seismic Hazard Mapping of Sea of Marmara (Istanbul, Turkey)

Based on a probabilistic approach, seismic risk in the Marmara (Turkey) region are quantified on a set of hazard maps that provide peak horizontal ground acceleration (PGA) and spectral acceleration at 0.2 sec, and 1.0 sec on rock site condition. These acceleration levels were computed for maximum credible earthquake for 2% and 10% probabilities of being exceeded in 50 years corresponding to return periods of about 2475 and 475 years, respectively. The maximum PGA computed (at rock site) is 1.5 g along the fault segments of the NAF zone extending into the Sea of Marmara. The new maps generally show 10% to 15% increase for PGA, 0.2 sec, and 1.0 sec spectral acceleration across much of Marmara compared to previous regional hazard maps. Hazard curves and smooth design spectra for three site conditions—rock, soil, and soft-soil—are provided for the Istanbul Metropolitan area as possible tools in future risk estimates.

DOCUMENTATION DOCUMENTATION IN TURKISH
Deterministic Seismic Design Values for Istanbul Metropolitan and Sea of Marmara (Turkey) Region

Istanbul, the largest urban sprawl in Turkey, is considered likely to experience a major earthquake during the next few decades. Using a deterministic approach, peak values of expected ground-motions are estimated for the Sea of Marmara (Turkey) region that encompasses the city based on six plausible earthquake scenarios. These scenarios consist of individual and multiple rupturing of the submarine fault segments along the western part of the North Anatolian Fault Zone (NAFZ) extending into the Sea of Marmara. To quantify the regional exposure on a set of hazard maps, a total of six ground motion prediction equations (GMPEs) have been used in a combinatorial approach to account for epistemic uncertainty. In lieu of subjectively weighting the expressions, the GMPEs were weighted proportional to their relative performance in predicting the measured peak ground motions of the 1999 M7.4 Kocaeli earthquake when it ruptured the Izmit segment of the NAFZ up to the eastern reaches of Istanbul. This computational approach has resulted in consistent but different weights for each GMPE at different spectral periods. The resultant high-resolution (0.002° by 0.002°, approx. 250 m by 250 m) deterministic seismic hazard maps, that implicitly incorporate site amplification due to softer sediments, provide peak horizontal ground acceleration (PGA) and spectral acceleration values at 0.2, 0.3, 0.5, 1, 1.5, 2, 3 and 4 seconds. The maximum spectral acceleration at 0.3 s computed is close to 1 g along the shoreline to the west of the Istanbul Metropolitan area, and 0.3 g near the financial district.

DOCUMENTATION

Ground-motion Selection, Scaling and Characterization

Required Number of Ground Motions for ASCE/SEI-7 Ground Motion Scaling Procedure

This study statistically examines the required number of records for the ASCE/SEI 7 procedure, such that the scaled records provide accurate, efficient, and consistent estimates of “true” structural responses. Based on elastic-perfectly-plastic and bilinear single-degree-of-freedom systems, the ASCE/SEI 7 scaling procedure is applied to 480 sets of ground-motions. The number of records in these sets varies from three to ten. The records in each set were selected either (i) randomly, (ii) considering their spectral shapes, or (iii) considering their spectral shapes and design spectral-acceleration value, A(Tn). As compared to benchmark (that is, “true”) responses from unscaled records using a larger catalog of ground-motions, it is demonstrated that the ASCE/SEI 7 scaling procedure is overly conservative if fewer than seven ground-motions are employed. Utilizing seven or more randomly selected records provides a more accurate estimate of the EDPs accompanied by reduced record-to-record variability of the responses. Consistency in accuracy and efficiency is achieved only if records are selected on the basis of their spectral shape and A(Tn).

DOCUMENTATION
Modal Pushover-based Ground Motion Scaling Procedure for Nonlinear Response History Analysis of Structures

Earthquake engineering practice is increasingly using nonlinear response history analysis (RHA) to demonstrate performance of structures. This analysis method requires selection and scaling of ground motions appropriate to design hazard levels. Presented herein is a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear RHA of buildings and bridges. In the MPS method, the ground motions are scaled to match (to a specified tolerance) a target value of the inelastic deformation of the first-”mode” inelastic single-degree-of-freedom (SDF) system whose properties are determined by first-”mode” pushover analysis. Appropriate for first-”mode” dominated structures, this approach is extended for structures with significant contributions of higher modes by considering elastic deformation of second-“mode” SDF system in selecting a subset of the scaled ground motions. Based on results presented for two bridges, covering single- and multi-span “ordinary standard” bridge types, and six buildings, covering low-, mid-, and tall building types in California, the accuracy and efficiency of the MPS procedure are established and its superiority over the ASCE/SEI 7-05 scaling procedure is demonstrated.

DOCUMENTATION
Modal Pushover-based Scaling Procedure for Nonlinear Response History Analysis of “Ordinary Standard” Bridges

The modal-pushover-based scaling (MPS) procedure (Kalkan and Chopra, 2010) recently was developed to determine scale factors for a small number of records, such that the scaled records provide accurate and efficient estimates of “true” median structural responses. The adjective “accurate” refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective “efficient” refers to the record-to-record variability of responses. Herein, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing “ordinary standard” bridges typical of reinforced-concrete bridge construction in California. These bridges are the single-bent overpass, multi span bridge, curved-bridge, and skew-bridge. As compared to benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the responses. Thus, the MPS procedure is a useful tool for scaling ground motions as input to nonlinear RHAs of “ordinary standard” bridges.

DOCUMENTATION
Experimental Evaluation of Ground Motion Scaling Methods for Nonlinear Analysis of Structural Systems

The study is based on the measured response from small-scale shake-table experiments of nonlinear multi-story building frame structures under ground motion suites that have been scaled using different methods. Four structural configurations with different fundamental periods and lateral strengths are investigated to assess the effectiveness of the scaling methods in reducing the dispersion in the seismic lateral displacement demands of the structures from a total of 720 shake-table tests. Four scaling methods are examined, including three methods that depend on a priori knowledge of the properties of the structure being analyzed, as well as a method based solely on the properties of the ground motions. The experimental results show that the method based solely on the properties of the ground motions generally produced demand results with less dispersion than the other evaluated scaling methods. However, the methods that rely on prior knowledge of the structure performed better at preserving the benchmark median demands for several of the cases considered.

DOCUMENTATION
Near-Fault Forward Directivity and Fling Effects on Building Structures

Near-fault ground motions are often characterized by coherent long-period velocity pulses that may result in sudden and extreme deformation demands in structural components. This study investigates the consequences of well-known characteristics of pulse-type motions on the seismic response of moment-frame steel buildings. The severity of inelastic demands was evaluated for four, six and thirteen-story existing steel buildings subjected to near-fault ground motions with fling-step and forward directivity, and compared to their response to far-fault ground motions. Additionally, idealized pulses are utilized in a separate evaluation study to gain further insight into the effects of high amplitude pulses on structural demands. Simple input pulses were also synthesized to simulate artificial fling-step effects on ground motions originally having forward directivity. Findings from the analytical simulations reveal that median maximum demands as well as the dispersion in the peak values for the three buildings were higher for near-fault records than far-fault motions. The arrival of the velocity pulse in a near-fault record causes the structure to dissipate considerable input energy in relatively few plastic cycles whereas cumulative effects from increased cyclic demands are more pronounced in far-fault ground motions. For pulse-type input, the maximum demand is a function of the ratio of the pulse period to the fundamental period of the structure. More significantly, records with fling effects were found to excite systems primarily in their fundamental mode while waveforms with forward directivity in the absence of fling caused higher modes to be activated.

DOCUMENTATION DATA SET

Basin Effect and Long Period Ground Motions

Long-Period (3 to 10 s) Ground Motions in and around the Los Angeles Basin during the 2010 M7.2 El Mayor-Cucapah Earthquake

We examined the characteristics of long-period strong ground motions within a period range of 3 to 10 s in and around the Los Angeles (LA) basin during the Mw7.2 El Mayor-Cucapah earthquake. The contour map of the observed peak ground velocity (PGV) values clearly shows that the LA basin significantly amplifies the long-period motions. The largest PGV values observed within the LA basin range from 0.1 to 0.12 m/s, though the basin is around 350 km away from the epicenter. These largest PGV values were recorded at seven stations in the central part, and one station in the western part of the basin. The Fourier acceleration spectra of records from these eight stations are predominant at the periods of 6 to 8 s with the corresponding peak values of 1 to 1.4 m/s. The ratio of Fourier amplitudes with respect to a reference site (STG station of the Southern California Seismic Network, located on hard rock in the southeast edge of the LA basin) show that the spectral amplitudes at these eight stations are 5 to 13 times larger than those at the reference site within a wide period range, 5.5 to 9 s.

DOCUMENTATION

MatLAB Functions

ASCE 41-06 DISPLACEMENT COEFFICIENT METHOD

MatLAB function for displacement coefficient method of ASCE 41-06 based on FEMA 440.

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AUTODETECT BANDPASS FILTER CORNER FREQUENCIES

Processing seismic waveforms often requires bandpass filtering. Selecting appropriate filter corner frequencies has been not only a manual process but also subjective. There is a need for automatically detecting corner frequencies for processing a large number of seismic recordings. cornerFreqs automatically detects appropriate bandpass filter corner frequencies by comparing the input signal's Fourier amplitude spectrum with that of the noise.

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AUTOMATIC P-PHASE ARRIVAL TIME PICKER

PphasePicker is a powerful tool for automatically picking P-phase onsets with high precision without requiring detection interval or threshold settings. The algorithm detects P-phase onset in single-component acceleration or broadband velocity records using the histogram method. It also computes signal-to-noise ratio (SNR). An example MatLAB code is provided in the zip file to show how to run PPHASEPICKER using three sample waveforms, one from strong motion and others from micro seismic events.

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AUTOMATIC S-PHASE ARRIVAL TIME PICKER

SphasePicker is a powerful tool for automatically picking S-phase onsets with high precision without requiring detection interval or threshold settings. The algorithm detects S-phase onset in single-component acceleration or broadband velocity records using the histogram method. It also computes signal-to-noise ratio (SNR). A demo file is provided in zip file to show how to run SPHASEPICKER using a sample waveform.

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COMPLEX MODE IDENTIFICATION FUNCTION (CMIF)

CMIF is defined as the Eigen values solved from the normal matrix, which is formed from frequency response function (FRF) matrix. CMIF can be computed from multiplication of normal matrix with its Hermitian matrix or by singular value decomposition (SVD) of normal matrix at each spectral line. This MatLAB function computes CMIF using "economy size" SVD. Bandpass filtering of input data is suggested before using CMIF.

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COMPUTE SMOOTH FOURIER AMPLITUDE SPECTRUM (MEDIAN AND RMS AVERAGING)

This function computes Fourier amplitude spectrum and its smoothed version. For smoothing, it uses window averaging based on median or rms value of the window. Default number of windows is twenty. The code also accepts a user-defined value for number of windows. Windows have equal number of data points.

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DECIMATE (DOWNSAMPLE) SIGNAL IN FREQUENCY DOMAIN

Frequency domain decimation function to reduce the original sampling rate of signal to a lower rate. A demo is presented in zip file, which compares decimateFD with MatLAB's downsample function.

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DECONVOLUTION OF TWO DISCRETE-TIME SIGNALS

A robust deconvolution function to study wave propagation. Low pass filtering and resampling the input signals to higher sampling rates may help to eliminate noise and improve pick peaking. An example MatLAB code with actual input signals to replicate the plot shown here is included in the zip file.

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DESPIKING DISCRETE TIME SERIES

Time series may contain undesired transients and spikes. This function replaces spikes (outliers) exceeding the threshold value by interpolating among previous and subsequent data points or replacement them with NaN per user choice. The threshold is defined as mean +/- a number of standard deviations of windowed data centered at spike locations. This code uses the histogram method of Solomon et al. (2001) to detect spikes. Examples are given in the comment section.

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Epoch & Unix Timestamp Converter (epoch2UTC)

A simple function that converts an epoch/unix timestamp into a human readable date.

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FREQUENCY DOMAIN WHITENING OF DISCRETE TIME-SIGNAL

This function generates flat Fourier spectrum for a given signal (which is originally not white) either for the full range of 0 Hz to the Nyquist frequency or for a user defined frequency band. This operation tends to sharpen signal, as well as the noise. The whitening process is often used for ambient vibration data before stacking waveforms for cross-correlation. The process is simple as Fourier transforming the signal after applying Hann window, then normalizing its magnitude, and then inverse Fourier transforming it.

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FREQUENCY DOMAIN ZERO-PADDING RESAMPLING (INTERPOLATION) OF DISCRETE-TIME SIGNAL

This function does the same as interpft of MatLAB, but it is much simpler and makes it easy to understand how the frequency domain zero padding (FDZP) resampling works

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FREQUENCY RESPONSE FUNCTION OF ACCELEROMETER (OSCILLATOR)

FRFaccelerometer computes transfer function of a single-degree-of-freedom system with damping and natural frequency. In a nutshell, this code generates the FRF of an accelerometer. An example MatLAB code is included.

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FREQUENCY-DOMAIN CROSS-CORRELATION FUNCTION

xcorrFD takes two discrete time signals as input and calculates cross-correlation values and delay between two signals. The computation is performed in the frequency domain. The results of xcorrFD is validated against the MatLAB's xcorr function. 

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FREQUENCY-DOMAIN DIFFERENTIATION OF DISCRETE TIME-SIGNAL

Robust MatLAB differentiation function to compute derivative of discrete time-signal in frequency domain by multiplying its Fourier spectrum with iw (w = cyclic frequency)

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FREQUENCY-DOMAIN INTEGRATION OF DISCRETE TIME-SIGNAL

Robust MatLAB function to integrate discrete time-signal in frequency domain by dividing its Fourier spectrum with -iw (w = cyclic frequency).

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GRAIZER-KALKAN 2015 GROUND-MOTION PREDICTION EQUATION

Graizer-Kalkan (2015) ground motion prediction equation (GMPE) is designed to predict peak-ground acceleration and 5% damped pseudo-spectral acceleration response ordinates for shallow-crustal continental earthquakes to be used in earthquake-engineering applications including probabilistic and deterministic seismic hazard analyses. The GK15 can be used for earthquakes with moment magnitudes 5.0–8.0, distances 0–250 km, average shear-wave velocities 200–1,300 m/s, and spectral periods 0.01–5 s. The GK15 GMPE is coded as a MatLAB function (titled “GK15.m”) in the zip file. An example MatLAB code (“demo.m”) to generate a 5% damped pseudo-spectral acceleration response spectrum for a given hazard condition is also provided. The user can change the input parameters to construct a site-specific response spectrum considering different hazard conditions.

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NONLINEAR-INELASTIC CONSTANT YIELD DISPLACEMENT RESPONSE SPECTRA

This code provides full set of functions to generate nonlinear-inelastic constant yield displacement spectra for acceleration, velocity and displacement. It also computes input energy parameters including relative and absolute total energy, kinetic energy, damping energy and hysteretic energy.

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NONLINEAR-INELASTIC CONSTANT YIELD MULTI-AXIAL RESPONSE SPECTRA CONSIDERING HORIZONTAL, VERTICAL AND ROTATIONAL MOTIONS

Robust function to generate multi-component constant-ductility nonlinear-inelastic response spectra for multi-axial simultaneous excitation including horizontal, vertical and rotational motions (i.e. rotational acceleration and tilt). It also computes components of seismic input energy imparted to the SDOF oscillator. 

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NONLINEAR-INELASTIC MULTI-AXIAL TIME RESPONSE ANALYSIS OF SDOF OSCILLATOR

Robust MatLAB function for nonlinear-inelastic time-history analysis of SDOF oscillator subjected to multi-axial simultaneous excitation including horizontal, vertical and rotational motions. It also computes components of seismic input energy imparted to SDOF oscillator. 

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NONLINEAR-INELASTIC RESPONSE HISTORY ANALYSIS OF SDOF OSCILLATOR USING OPENSEES

Fast MatLAB function for nonlinear-inelastic time-history analysis of a single-degree-of-freedom (SDOF) oscillator. The code runs for a single or a series of input excitations for parametric study. MatLAB is used for pre-processing; nonlinear SDOF system is constructed and solved using OpenSEES (http://opensees.berkeley.edu/index.php) in the background. 

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P-PHASE ARRIVAL TIME PICKER BASED ON AKAIKE INFORMATION CRITERION

Computes P-phase arrival time in windowed digital single-component acceleration or broadband velocity record without requiring threshold settings using AKAIKE INFORMATION CRITERION. Returns P-phase arrival time index.

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PIECEWISE CUBIC SPLINE INTERPOLATION

Two functions (for constructing and evaluating the spline function) written originally in C language in NUMERICAL RECIPES were adapted for MatLAB. A clear example is provided in "demo.m", which compares the results with the MatLAB's spline function's outcome. 

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PSEUDO SPECTRAL ACCELERATION, VELOCITY AND DISPLACEMENT SPECTRA

This MatLAB function generates pseudo-spectral acceleration (PSA), pseudo-spectral velocity (PSV) and spectral displacement (SD) spectra for given damping ratio (e.g., 5% of critical). Spectral ordinates are for linear-elastic single-degree-of-freedom system with unit mass. A clear example is provided in demo.m file in zipped folder. Also provided is a plotting function for PSA, PSV and SD spectra.

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SMOOTHING FUNCTION FOR FOURIER AMPLITUDE SPECTRUM (KONNO-OHMACHI WINDOW)

smoothCurve offers various different window smoothing options. Default window function is Konno-Ohmachi, which is symmetric in log space. This function uses convolution method to filter the signal for smoothing.

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TIME-DOMAIN CROSS-CORRELATION FUNCTION

xcorrTD takes two discrete time signals as input and calculates cross-correlation values, cross-correlation coefficients and delay (lag) between two signals. The computation is performed in the time domain. The results of xcorrTD has been validated against the MatLAB's xcorr function.

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TIME-DOMAIN SINC INTERPOLATION (RESAMPLING)

A robust interpolation function using a SINC kernel to convolve the original input time series in order to get resampled time series. A simple example is provided in comment section to illustrate how resampleSINC works.

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