Constituent Frequency Research Articles

The effect of constituent frequency and distractor type on learning novel complex words

ABSTRACT The present study explored the role of constituent frequency and distractor type in complex word learning. Skilled readers were trained to associate novel letter strings with one out of two pictures, with one picture serving as the target, and the other as a distractor. A facilitatory effect of first-constituent frequency was found only in trials where distractors promoted first-constituent learning, and a facilitatory effect of second-constituent frequency only in trials where distractors promoted second-constituent learning, but not vice versa. Learning occurred in the absence of any pre-existing knowledge about the constituent morphemes and any explicit reference to the constituents during learning. The results point to the important role of constituent frequency and distractor type in novel word learning and provide insights into the mechanisms involved in the implicit acquisition of morphological knowledge in adult learners, that we suspect to be a key aspect of language learning in general.

Wolf-hound vs. sled-dog: neurolinguistic evidence for semantic decomposition in the recognition of German noun-noun compounds.

Animacy is an intrinsic semantic property of words referring to living things. A long line of evidence shows that words with animate referents require lower processing costs during word recognition than words with inanimate referents, leading among others to a decreased N400 amplitude in reaction to animate relative to inanimate objects. In the current study, we use this animacy effect to provide evidence for access to the semantic properties of constituents in German noun-noun compounds. While morphological decomposition of noun-noun compounds is well-researched and illustrated by the robust influence of lexical constituent properties like constituent length and frequency, findings for semantic decomposition are less clear in the current literature. By manipulating the animacy of compound modifiers and heads, we are able to manipulate the relative ease of lexical access strictly due to intrinsic semantic properties of the constituents. Our results show additive effects of constituent animacy, with a higher number of animate constituents leading to gradually attenuated N400 amplitudes. We discuss the implications of our findings for current models of complex word recognition, as well as stimulus construction practices in psycho-and neurolinguistic research.

Relative pitch representations and invariance to timbre

Information in speech and music is often conveyed through changes in fundamental frequency (f0), perceived by humans as “relative pitch”. Relative pitch judgments are complicated by two facts. First, sounds can simultaneously vary in timbre due to filtering imposed by a vocal tract or instrument body. Second, relative pitch can be extracted in two ways: by measuring changes in constituent frequency components from one sound to another, or by estimating the f0 of each sound and comparing the estimates. We examined the effects of timbral differences on relative pitch judgments, and whether any invariance to timbre depends on whether judgments are based on constituent frequencies or their f0. Listeners performed up/down and interval discrimination tasks with pairs of spoken vowels, instrument notes, or synthetic tones, synthesized to be either harmonic or inharmonic. Inharmonic sounds lack a well-defined f0, such that relative pitch must be extracted from changes in individual frequencies. Pitch judgments were less accurate when vowels/instruments were different compared to when they were the same, and were biased by the associated timbre differences. However, this bias was similar for harmonic and inharmonic sounds, and was observed even in conditions where judgments of harmonic sounds were based on f0 representations. Relative pitch judgments are thus not invariant to timbre, even when timbral variation is naturalistic, and when such judgments are based on representations of f0.

A Filter-Less Time-Domain Method for Reference Signal Extraction in Shunt Active Power Filters

Current distortion degrades power quality and affects system performance, especially for sensitive loads that require pure sinusoidal waves. Owing to its excellent dynamic response, a well-designed active power filter (APF) can achieve a total harmonic distortion (THD) within the acceptable limits defined by IEEE 3002 standards through compensating harmonic distortions. The APF consists of two main modules: a reference signal extraction module and a modulation module. This paper adapts the matrix pencil method, a well-known model-based parameter estimation technique, to the problem of reference extraction. Contrary to conventional time-domain methods such as the synchronous reference frame (SRF) and the reactive power theory (PQ theory) that rely on low-pass filters in their implementations, the proposed method does not use a filter. However, it extracts the reference signal by first decomposing the load current into its constituent frequency components, and then subtracting the pure sine wave synthesized from the obtained fundamental component from the load current. Results on simulated data from MATLAB/Simulink confirm the higher accuracy and fast response time of the proposed method in extracting the reference signal.

LTP Modeling and Stability Assessment of Multiple Second-Order Generalized Integrator-Based Signal Processing/Synchronization Algorithms and Their Close Variants

A second-order generalized integrator (SOGI) is a resonant regulator with a pair of complex-conjugate poles, and therefore, with infinite magnitude at its center frequency. Thanks to this property, one can put together a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> SOGIs in an elegant way and decompose a single-phase signal into its constituent frequency components and detect their amplitude and phase angle. Such a configuration, which is often referred to as the multi-SOGI (MSOGI) structure, requires a frequency estimator to adapt the center frequency of SOGIs to frequency changes. This frequency estimation is often provided by interconnecting the MSOGI structure with a basic frequency-locked loop (FLL) or phase-locked loop (PLL). The resulting structures are known as the MSOGI-FLL and MSOGI-PLL. These structures and their close variants are mathematically difficult to analyze probably because of the lack of a linear model for these systems. This article aims to bridge this research gap. First, it is shown how linear time-periodic (LTP) models of the MSOGI-FLL and MSOGI-PLL can be obtained. The model verification, obtaining open-loop harmonic transfer function from the LTP model, and LTP stability assessment of MSOGI-based synchronization systems are the next parts of this article. Finally, some close variants of the MSOGI-FLL/PLL are considered and their modeling and stability assessment are briefly discussed.

Simulating the stratigraphy of meandering channels and point bars of Cretaceous system using spectral decomposition tool, Southwest Pakistan: Implications for petroleum exploration

Fluvial channels (FC) and point bars sandstone (PDs) sedimentary fills form primary brilliant stratigraphic petroleum systems within the transgressive system tract (TST). They are developed during the rapid rise and subsequent standstill of sea-level, which fills the reservoirs with FC and PD. These petroleum systems are ultra-thin-bedded (UTB) due to the very small vertical thickness of TST within the complete depositional sequences. Hence, they create hurdles in the prediction of lithology and porosity for these stratigraphic traps. The continuous wavelet transform (CWT) is the only sub-surface seismic imaging tool of spectral decomposition that can resolve the thin-beds of petroleum-bearing stratigraphic traps. This method removes the tuning effects of ambiguous lithology and fluids that masks the reservoir zones, and hence, generates false bright spots. This method decomposes the conventional seismic data into its constituent frequency components without fixing the vertical time window for the stratigraphic systems. These frequency components are further used for the prediction of lithology and porosity for resolving sub-surface depositional systems. Therefore, the CWT has delineated the fluvial sandstone facies, fractures connectivity, and architecture of the fluvial depositional system during the sea-level fluctuations. The 48-Hz has imaged the regional standstill of sea level, which have accumulated the porous sedimentary facies of coarse-grained FC andPDs. A very local sea-level rise was imaged in the eastern to the central part of this petroleum system. This sea-level fluctuation has implicated that there were minor cycles of transgressive sea-level, which has developed a pure stratigraphic play. The trace envelope attribute experienced a poor correlation coefficient with R2<0.2. The 48-Hz CWT experienced a correlation coefficient of R2>0.91 for FC and PDs. The conventional inverted reservoir simulation has imaged the low-frequency variance inside ~15-31% porous zones of FC and PDs. The 48-Hz volume has imaged the laterally continuous and hydrocarbon-bearing reservoirs with >25% porosity. 48-Hz CWT model also has imaged the coarse-grained FC of aggradational meandering channel stream, which were implicated to develop during stand-still of sea-level. These sandstone lenses were enclosed at the top by progradational shale facies of the highstand system tract (HST) and bottom and lateral by the shales of the TST. This workflow serves as an analogue within the SE-Asian sedimentary Basins and similar worldwide geological basins.

Enhancement of time-frequency post-processing readability for nonstationary signal analysis of rotating machinery: Principle and validation

Rotating machinery signals are often composed of multiple components and are nonstationary under practical time-varying conditions. In most cases, the constituent frequency components are close to each other on time–frequency plane. As such, better time–frequency readability is necessary to discover the underlying physical nature of such complex nonstationary signals. Nevertheless, conventional time–frequency analysis methods suffer from limited time–frequency resolution and/or cross-term interferences, thus cannot achieve desirable time–frequency readability. In recent decades, some time–frequency post-processing methods (such as time–frequency reassignment, synchrosqueezing transform, multi-tapering, concentration of frequency and time, and higher-order synchrosqueezing transform) have been proposed to improve the time–frequency readability from two aspects: reducing cross-term interferences and enhancing time–frequency energy concentration. However, they still surfer from time-frequency blurs for the signal whose time–frequency ridges are close to each other on time–frequency plane. To address this issue, we propose a framework to improve the post-processing methods. Firstly, the Vold-Kalman filter is employed to extract constituent frequency components, by exploiting its capability to separate mono-components. Then, the time–frequency representation (TFR) of each mono-component is obtained via time–frequency post-processing method separately. Finally, the TFR of raw signal is constructed by superposing the TFR of all mono-components. This framework achieves a TFR of high time–frequency resolution, free from cross-term interferences, and therefore better time–frequency readability. As such, it extends time–frequency post-processing methods to analyze complex nonstationary signals. The proposed framework is illustrated through numerical simulation, and validated using typical rotating machine vibration data (including the experimental signals of a planetary gearbox and an induction motor, ground test data of a civil aircraft engine and in-situ measurement of a hydraulic turbine rotor). The analysis results show the good capability of proposed framework to reveal the frequency contents and their time-varying features of complex nonstationary signals.

The constraints between amino acids influence the unequal distribution of codons and protein sequence evolution.

Four nucleotides (A, U, C and G) constitute 64 codons at free combination but 64 codons are unequally assigned to 21 items (20 amino acids plus one stop). About 500 amino acids are known but only 20 are selected to make up the proteins. However, the relationships between amino acid and codon and between 20 amino acids have been unclear. In this paper, we studied the relationships between 20 amino acids in 33 species and found there were three constraints between 20 amino acids, such as the relatively stable mean carbon and hydrogen (C : H) ratios (0.50), similarity interactions between the constituent ratios of amino acids, and the frequency of amino acids according with Poisson distribution under certain conditions. We demonstrated that the unequal distribution of 64 codons and the choice of amino acids in molecular evolution would be constrained to remain stable C : H ratios. The constituent ratios and frequency of 20 amino acids in a species or a protein are two determinants of protein sequence evolution, so this finding showed the constraints between 20 amino acids played an important role in protein sequence evolution.

Feature Extraction And Sound Pattern Analysis Of Wijaaksara Script

Wijaksara script is a sacred script in the Balinese script structure in Balinese Hindu culture, the sound of this script is believed to create vibrations that are spiritual and magical. In Balinese script literature, Wijaksara script is a combination of the Swalatita script with the Amsa script. Wijaksara script are categorized into several groups, namely (1) Eka Aksara (Om), (2) Dwi aksara (Ang, Ah), (3) Tri Aksara (Ang, Ung, Mang), (4) Panca Aksara (Nang, Mang, Sing, Wang, Yang), and (5) Dasa Aksara (Sang, Bang, Tang, Ang, Ing, Nang, Mang, Sing, Wang, Yang). In this research, several acoustic features of sound were extracted (1) constituent frequencies, (2) waveforms, (3) sound energy. Sound recordings from 20 samples were taken and then extracted to get the constituent frequency using FFT (Fast Fourier Transform). Based on the sound waveform, the waveform and sound energy are obtained. In this study, the acoustic character patterns were obtained, namely Eka, Dwi, Tri, Panca, and Dasa. Aksara is influenced by the sound character of the eka script. The main frequencies for the sounds of the letters eka, bi, tri, and dasa are: 4.37 kHz, 7.22 kHz, 3.97 kHz. 4.18 KHZ, 11.8 KHz, while the sound energy for normal sound pronunciation conditions are: 87.31 dB, 96.72 dB, 83.25 dB, and 80.29 dB, respectively.

An eye-tracking study of reading long and short novel and lexicalized compound words.

An eye-tracking experiment examined the recognition of novel and lexicalized compound words during sentence reading. The frequency of the head noun in modifier-head compound words was manipulated to tap into the degree of compositional processing. This was done separately for long (12–16 letter) and short (7-9 letters) compound words. Based on the dual-route race model [Pollatsek et al., 4] and the visual acuity principle [Bertram & Hyönä, 2], long lexicalized and novel compound words were predicted to be processed via the decomposition route and short lexicalized compound words via the holistic route. Gaze duration and selective regression-path duration demonstrated a constituent frequency effect of similar size for long lexicalized and novel compound words. For short compound words the constituent frequency effect was negligible for lexicalized words but robust for novel words. The results are consistent with the visual acuity principle that assumes long novel compound words to be recognized via the decomposition route and short lexicalized compound words via the holistic route.

CompLex: an eye-movement database of compound word reading in English.

The CompLex database presents a large-scale collection of eye-movement studies on English compound-word processing. A combined total of 440 participants completed eye-tracking experiments in which they silently read unspaced English compound words (e.g., goalpost) embedded in sentence contexts (e.g., Dylan hit the goalpost when he was aiming for the net.). Three studies were conducted using participants representing the non-college-bound population (300 participants), and four studies included participants recruited from the student population (140 participants). The database comprises trial-level eye-movement data (47,763 trials), participant data (including a measure of reading experience estimated via the Author Recognition Test), and lexical characteristics for the set of 931 English compound words used as critical stimuli in the studies. One contribution of the present paper is a set of regression analyses conducted on the full database and individual experiments. We report that the most reliable and consistent main effects were those elicited by compound word length, left constituent frequency, right constituent frequency, compound frequency and semantic transparency. Separately, we also found that the effect of left frequency and compound word length is weaker among more frequent compounds. Another contribution is a power analysis, in which we determined the sample sizes required to reliably detect effect sizes that are comparable to those observed in our regression models. These sample size estimates serve as a recommendation for researchers wishing to either collect eye-movement data for compound word reading, or use the current database as a resource for the study of English compound word processing.

Frequency decomposition and phase synchronization of the visual evoked potential using the empirical mode decomposition.

Objectives The phase characteristics of the representative frequency components of the Electroencephalogram (EEG) can be a means of understanding the brain functions of human senses and perception. In this paper, we found out that visual evoked potential (VEP) is composed of the dominant multi-band component signals of the EEG through the experiment. Methods We analyzed the characteristics of VEP based on the theory that brain evoked potentials can be decomposed into phase synchronized signals. In order to decompose the EEG signal into across each frequency component signals, we extracted the signals in the time-frequency domain with high resolution using the empirical mode decomposition method. We applied the Hilbert transform (HT) to extract the signal and synthesized it into a frequency band signal representing VEP components. VEP could be decomposed into phase synchronized δ, θ, α, and β frequency signals. We investigated the features of visual brain function by analyzing the amplitude and latency of the decomposed signals in phase synchronized with the VEP and the phase-locking value (PLV) between brain regions. Results In response to visual stimulation, PLV values were higher in the posterior lobe region than in the anterior lobe. In the occipital region, the PLV value of theta band was observed high. Conclusions The VEP signals decomposed into constituent frequency components through phase analysis can be used as a method of analyzing the relationship between activated signals and brain function related to visual stimuli.

Generalized adaptive mode decomposition for nonstationary signal analysis of rotating machinery: Principle and applications

Abstract Rotating machinery signals are usually intricate and often nonstationary. The analysis of such signals is further complicated because of the spectral overlaps between constituent frequency components under time-varying running conditions. Most conventional signal processing methods are unable to effectively extract the embedded meaningful information. Adaptive mode decomposition (AMD) methods are flexible to describe complex signals, free from the limitations inherent in conventional basis expansion and thus more suited to unveiling the underlying physical nature. However, as those methods work in a way similar to filter banks, i.e. via rectangular partition of time-frequency plane, they are effective only for signals with constituent frequency components that are almost constant and parallel to each other. As such, it would be inappropriate to apply such methods when signal constituent frequency components vary considerably over time and particularly overlap in frequency domain. To address this issue, this paper proposes a general framework by exploiting the unique capability of generalized demodulation to transform an arbitrary time-varying instantaneous frequency into a constant frequency. In doing so, many state-of-the-art AMD methods (including empirical mode composition, local mean decomposition, intrinsic time-scale decomposition, local characteristic scale decomposition, Hilbert vibration decomposition, empirical wavelet transform, variational mode decomposition, and adaptive local iterative filtering) can be extended to analyze highly nonstationary complex signals with spectral overlaps. The principle and advantage of generalized adaptive mode decomposition (GAMD) are illustrated through numerical simulation. The GAMD’s performance in monitoring different rotating machinery components (including a planetary gearbox, an aircraft engine rolling bearing and a hydraulic turbine rotor) is demonstrated and validated under time-varying conditions.

Compound reading in German: Effects of constituent frequency and whole-word frequency in children and adults.

Current models of morphological processing differ in their assumptions about the recognition of compound words. The relative contribution of the first and second constituent and the whole-word remains unsolved. Particularly for beginning readers, the first constituent might have a privileged role attributable to more sequential decoding strategies. In a series of lexical decision experiments, the influence of constituent and whole-word frequencies on compound recognition was examined in German developing readers as well as adults. Results showed that whole-word and first constituent frequency interactively influenced response times in children. For adults, an effect of whole-word frequency only was obtained for the children's stimuli set, and noninteracting effects of whole-word frequency and first constituent frequency were found when using adult frequency measures. Together, the results suggest that developing readers already decompose compounds and that hybrid interactive models of morphological processing are most suitable to explain compound recognition across development. The applicability of amorphous models is also discussed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Constituent frequency effects in the written production of Spanish compound words.

The debate about whether compound words are accessed as whole words or via their constituents remains unresolved, especially in the field of language production. In this study, three experiments used a copying task to examine whether compound words are accessed via their constituents in handwriting production. In Experiment 1, production of compound words and noncompounds was compared. The last interletter interval within the first constituent of compounds was observed to be shorter than the same interval in noncompounds, revealing that writing durations are sensitive to morphological processing. In Experiments 2 and 3, the first and second constituent frequency was manipulated respectively. The frequency of both constituents affected writing onset times. Interestingly, the interval between the last two letters of the first constituent was shorter when the second constituent wasof high frequency, suggesting that the effect obtained in this position in Experiment 1 was related to the anticipation of the second constituent. Our findings indicate that both constituents are activated before the initiation of the written response and that the second component is reactivated before the production of the first constituent has finished.

What does constituent priming mean in the investigation of compound processing?

Abstract Most dictionary definitions for the term compound word characterize it as a word that itself contains two or more words. Thus, a compound word such as goldfish is composed of the constituent words gold and fish. In this report, we present evidence that compound words such as goldfish might not contain the words gold and fish, but rather positionally bound compound constituents (e.g., gold- and -fish) that are distinct and often in competition with their whole word counterparts. This conceptualization has significant methodological consequences: it calls into question the assumption that, in a traditional visual constituent priming paradigm, the participant can be said to be presented with constituents as primes. We claim that they are not presented with constituents. Rather, they are presented with competing free-standing words. We present evidence for the processing of Hebrew compound words that supports this perspective by revealing that, counter-intuitively, prime constituent frequency has an attenuating effect on constituent priming. We relate our findings to previous findings in the study of German compound processing to show that the effect that we report is fundamentally morphological rather than positional or visual in nature. In contrast to German in which compounds are always head-final morphologically, Hebrew compounds are always head initial. In addition, whereas German compounds are written as single words, Hebrew compounds are always written with spaces between constituents. Thus, the commonality of patterning across German and Hebrew is independent of visual form and constituent ordering, revealing, as we claim, core features of the constituent priming paradigm and compound processing.

Amplitude-activated mechanical wave manipulation devices using nonlinear metamaterials

We report device implications for acoustic metamaterials with various nonlinear oscillator microstructures as passive amplitude-activated mechanical wave filters and waveguides using simulations on their representative one-dimensional discrete element models. Linear and various nonlinear hardening and softening stiffness cases and combinations thereof are considered for the local oscillators. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range are found to correspond to the excitation amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. Three passive acoustic devices—(i) amplitude-activated selective filter, (ii) amplitude band pass or band rejection filter, and (iii) direction-biased waveguide—are demonstrated numerically. Constituent frequency components in bifrequency excitations are shown to be retained or diminished to varying degrees within acoustic metamaterials with either hardening or softening local oscillators depending on their individual amplitudes. Using trilinear hardening or softening oscillators instead switches the response between attenuation and propagation respectively, outside of a tunable bandwidth of amplitude for the same excitation frequency. Whereas, amplitude-dependent, passive direction-bias in propagation characteristics for a given excitation frequency is demonstrated in a metamaterial waveguide composed of units with tuned combinations of linear and nonlinear hardening oscillators deployed in sequence. These predictions indicate the possibility of realizing acoustic metamaterials having passive adaptive, amplitude-activated dynamics using tailored combinations of nonlinear oscillators to elicit prescribed wave transformations across them.

Orbital angular momentum filter based on multiple-beam interference

Abstract By virtue of multiple-beam interference, periodic structures such as photonic or phononic crystals can be used to separate an incident polychromatic light or acoustic beams, respectively, into their constituent frequency components. In addition, it is widely acknowledged that a light beam that is carrying orbital angular momentum (OAM) also has a spatial angular frequency in the azimuthal zone. Here we demonstrate that multiple-beam interference in the azimuthal zone can be used to modulate the transmission of the OAM state and; can thus serve as an OAM filter. The 2 D transmission spectrum is analyzed and the mode resolution is discussed in detail. We anticipate that this OAM filter will be promising for use in applications such as optical switches, mode de-multiplexing in mode-division multiplexing communications and single-photon discrimination when using linear optical elements.

Quantification of Feto-Maternal Heart Rate from Abdominal ECG Signal Using Empirical Mode Decomposition for Heart Rate Variability Analysis

In this paper, a robust method of feto-maternal heart rate extraction from the non-invasive composite abdominal Electrocardiogram (aECG) signal is presented. The proposed method is based on the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) method, in which a composite aECG signal is decomposed into its constituent frequency components called Intrinsic Mode Functions (IMFs) or simply “modes”, with better spectral separation. Decomposed IMFs are then selected manually according to probable maternal and fetal heart rate information and are processed further for quantification of maternal and fetal heart rate and variability analysis. The proposed method was applied to aECG recordings collected from three different sources: (i) the PhysioNet (adfecgdb) database; (ii) the PhysioNet (nifecgdb) database; and (iii) synthetic aECG signal generated from mathematical modeling in the LabVIEW software environment. An overall sensitivity of 98.83%, positive diagnostic value of 97.97%, accuracy of 96.93% and performance index of 96.75% were obtained in the case of Maternal Heart Rate (MHR) quantification, and an overall sensitivity of 98.13%, positive diagnostic value of 97.62%, accuracy of 95.91% and performance index of 95.69% were obtained in case of Fetal Heart Rate (FHR) quantification. The obtained results confirm that CEEMDAN is a very robust and accurate method for extraction of feto-maternal heart rate components from aECG signals. We also conclude that non-invasive aECG is an effective and reliable method for long-term FHR and MHR monitoring during pregnancy and labor. The requirement of manual intervention while selecting the probable maternal and fetal components from “n” number of decomposed modes limits the real-time application of the proposed methodology. This is due to the fact that the number of modes “n” produced by the CEEMDAN decomposition is unpredictable. However, the proposed methodology is well suited for applications where a small time-delay or offset in feto-maternal monitoring can be acceptable. In future, application-specific modification of the CEEMDAN algorithm can be implemented to eliminate manual intervention completely and will be suitable for long-term feto-maternal monitoring.

Dynamic Response of a Defected Periodic Viaduct to a Moving Point Load

A defected periodic viaduct (DPV) is an infinite viaduct consisting of a left and a right semi-infinite ordered periodic viaducts (OPV) and one or several in-between defected spans different from the standard span of the OPV. Currently, no methodology is available in the literature for assessing the dynamic response of a DPV to a moving load, as the presence of the defected spans breaks the periodicity of the OPV. In this study, a new FEM model for estimating the dynamic response of a DPV with one defected span to a moving load is proposed. To establish the model, the time-space domain (TSD) moving load is decomposed into the sum of its constituent frequency wavenumber domain (FWD) load components first. For the DPV subjected to the FWD load component, the response of the left and right semi-infinite OPVs of the DPV can be divided into two parts, namely, the free wave field and the scattered wave field. To determine the free wave field of the left and right semi-infinite OPVs of the DPV, the FEM equations for an individual span of the viaduct are established and applied to the two OPVs. The scattered wave field in the two semi-infinite OPVs consists of the characteristic waves of the OPV and can be determined using the FEM eigenvalue equations for the OPV free of external loads. Applying the span FEM equations to the defected span and using the expressions for the free wave field and the scattered wave field yield the FWD response of the DPV. The time-space domain response of the DPV can then be retrieved by superposing all the FWD responses of the DPV. Numerical simulations are conducted to investigate the influence of the defected span on the dynamic response of the DPV. For the DPV, there are two kinds of the resonant frequencies, namely, the resonant frequencies common to the corresponding OPV and the additional resonant frequencies due to the presence of the defected span. In some cases, the magnitudes of the responses at the additional resonant frequencies may be larger than those at the common resonance frequencies. Therefore, when conducting the design for a periodic viaduct, it is important to account for the influence of the defected span on the dynamic response of the periodic viaduct.