Fundamental Frequency Estimation Research Articles

Single-cycle P Class phasor estimation based on harmonics whitening and off-nominal frequency offset adjustment

Phasor Measurement Units (PMUs) are essential for real-time power system monitoring and control. In this paper, a novel algorithm for protection (i.e., P Class) PMUs is presented. The proposed algorithm consists of four steps: preliminary narrowband disturbance whitening; estimation of the off-nominal fundamental frequency offset through the Interpolated Discrete Time Fourier Transform (IpDFT); data record length adjustment to refine narrowband disturbance whitening over an integer number of fundamental periods; time-domain estimation of the Taylor's series coefficients of the synchrophasor function through a weighted least-squares estimator (after correction of possible static off-nominal deviations). The key novel contribution of the proposed approach is its superior ability to smooth harmonic disturbances over shorter observation intervals than many existing algorithms (which typically require at least two-cycle-long data records to meet P Class accuracy requirements), while ensuring a good tracking capability of transient events with a reasonable execution time. Several simulation and experimental results confirm that, in the case of multi-harmonic distortion, the proposed approach returns more accurate results than both the basic Taylor-series-based Weighted Least-Squares (TWLS) estimator and other whitening-based techniques, while ensuring compliance with P Class specifications even over one-cycle-long data records.

Multiparametric Analysis of Speaking Fundamental Frequency in Genetically Related Speakers Using Different Speech Materials: Some Forensic Implications.

To assess the speaker-discriminatory potential of a set of fundamental frequency estimates in intraidentical twin pair comparisons and cross-pair comparisons (i.e., among all speakers). A total of 20 Brazilian Portuguese speakers of the same dialect, namely 10 male identical twin pairs aged between 19 and 35, were recruited. The participants were recorded directly through professional microphones while taking part in a spontaneous dialogue over mobile phones. Acoustic measurements were performed in connected speech samples, and in lengthened vowels, at least 160ms long produced during spontaneous speech. f0 baseline, central tendency, and extreme values were found mostly discriminatory in intra-twin pair and cross-pair comparisons. These were also the estimates displaying the largest effect sizes. Overall, only three identical twins were found statistically different regarding their f0 patterns in connected speech, but not for lengthened vowel-based f0 metrics. Estimates of f0 variation and modulation were found the least discriminatory across speakers, which may signal the control of speaking style and dialect on dynamic patterns of f0. Concerning system performance, the base value of f0 (f0 baseline) was found the most reliable metric, displaying the lowest equal error rate (EER). The outcomes suggest that, although identical twins were very closely related regarding their f0 patterns, some pairs could still be differentiated acoustically, only in connected speech. Such findings reinforce the relevance of analyzing long-term f0 metrics for speaker comparison purposes, with particular consideration to f0 baseline. Furthermore, f0 differences across subjects were suggested as more expressive in connected speech than in lengthened vowels.

Quantum computing for solid mechanics and structural engineering – A demonstration with Variational Quantum Eigensolver

Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that recently became accessible to the worldwide research community. Here, we implement and demonstrate the numerical processes on the 5-qubit and 7-qubit quantum processors on the IBM Qiskit Runtime platform. We combine the commercial finite-element-method (FEM) software ABAQUS with the implementation of Variational Quantum Eigensolver (VQE) to establish an integrated pipeline. Three examples are used to investigate the performance: a hexagonal truss, a Timoshenko beam, and a plane-strain continuum. We conduct parametric studies on the convergence of fundamental natural frequency estimation using this hybrid quantum-classical approach. Our findings can be extended to problems with many more degrees of freedom when quantum computers with hundreds of qubits become available in the near future.

Characterization of Site Amplification by a Parametric Study

ABSTRACT The reliability of V s30 and the performance of alternative time averaged shear wave velocities (V sz ) and shear wave travel times (T tz ) at various depths, z, were investigated for the estimation of site amplification and fundamental frequency (f 0) characterization by considering the linear and nonlinear soil behavior. The study revealed that alternative parameters performed better than V s30 and the best performing z parameters changed by switching from convex to concave theoretical profiles and by increasing ground motions. For a practical usage in site investigations, guidelines to estimate nonlinear soil amplification factor and fundamental frequency from the linear ones were presented.

Multipitch estimation based on the iterative detection and separation of note events from single-channel polyphonic recordings.

Multiple fundamental frequency estimation has been extensively used in applications such as melody extraction, music transcription, instrument identification, and source separation. This paper presents an approach based on the iterative detection and extraction of note events, which are considered to be harmonic sounds characterised by a continuous pitch trajectory. Note events are assumed to be associated with musical notes being played by a single instrument, and their pitch trajectories are iteratively estimated. In every iteration, the pitch contour of the predominant note event is selected from a set of pitch estimates and used to separate its spectral energy from the input mixture in order to obtain a residual signal, which is then used as input in the next iteration. This iterative process stops when the energy of the residual is below a significance threshold. The pitch trajectories of all detected note events are then revised and reassembled to form the final set of pitch estimates for the original audio input. Evaluation of performance is conducted in different scenarios to show the potential of the proposed system, both in terms of its accuracy, and also as an initial stage in other complex tasks, such as note tracking and multipitch streaming.

Advanced Diagnostic Approach for High-Voltage Insulators: Analyzing Partial Discharges through Zero-Crossing Rate and Fundamental Frequency Estimation of Acoustic Raw Data

Acoustic inspection is a valuable technique that can detect early stage defects in equipment, thereby facilitating predictive maintenance. In recent times, ultrasonic sensors have made detecting partial discharges through acoustic sensing increasingly feasible. However, interpreting the acoustic signals can pose challenges, as it requires extensive expertise and knowledge of equipment configuration. To address this issue, a technique based on zero-crossing rate and fundamental frequency estimation has been proposed to standardize insulator diagnosis. In an experiment involving a database of 72 raw acoustic signals with frequencies ranging from 0 to 128 kHz, various types of pollution and defects were introduced to a chain of insulators. By employing the proposed technique, the occurrence of partial discharges can be detected and classified according to type, such as corona or surface discharges. This advanced approach to diagnosis simplifies the process while providing valuable insights into the severity of observed phenomena in the field.

Reducing the uncertainties in the NGA-West2 ground motion models by incorporating the frequency and amplitude of the fundamental peak of the horizontal-to-vertical spectral ratio of surface ground motions

Ground motion models (GMMs) are developed empirically to predict ground motion intensity measures. The site effects in GMMs are usually addressed using time-averaged shear-wave velocity for the upper 30 m of the site (VS30) and shear-wave isosurface depth (i.e. Z1.0 and Z2.5). However, the former does not include the effect of layered soil structure on the site’s response, and the latter is generally inferred. Many studies have shown that site fundamental frequency can be used as an additional site proxy. Using horizontal-to-vertical spectral ratio (HVSR), one can estimate the site fundamental frequency in a fast and inexpensive way. In this article, a model is developed to incorporate site fundamental frequency and its corresponding amplification factor in the Next Generation Attenuation (NGA)-West2 GMMs to reduce the uncertainties. First, a subset of the NGA-West2 database consisting of 14,636 recordings from 298 events is selected after a two-step screening procedure and used to compute the horizontal-to-vertical response spectral ratio (HVSRPSA) of recorded surface ground motions. Second, automated methodologies previously developed by the authors are used to obtain maximum likelihood estimates of site fundamental frequency (fml), its corresponding amplitude (Aml), and associated uncertainties. Third, a mixed-effect maximum likelihood approach is implemented for residual analysis and site-term residual calculation. Finally, an HVSR-based model is developed for the NGA-West2 dataset considering the relationship between site-term residual and the HVSR-based proxies (i.e. fml and Aml). In this model, Aml is as important as fml in reducing the uncertainties. Results show that using a single HVSR-based model can consistently reduce the site-to-site variability ([Formula: see text]) for all NGA-West2 GMMs, which already include the effect of VS30, Z1.0, or Z2.5. Besides, the reduction in [Formula: see text] is period-dependent, with an average of 13% reduction. As a result of the reduction in [Formula: see text], total standard deviation ( σ) decreases by 3.5% on average.

Knee Flexion-Assisted Method for Human-Exoskeleton System.

The knee has gradually become an important research target for the lower extremity exoskeleton. However, the issue that whether the flexion-assisted profile based on the contractile element (CE) is effective throughout the gait is still a research gap. In this study, we first analyze the effective flexion-assisted method through the passive element's (PE) energy storage and release mechanism. Specifically, ensuring assisting within an entire joint power period and the human's active movement is a prerequisite for the CE-based flexion-assisted method. Second, we design the enhanced adaptive oscillator (EAO) to ensure the human's active movement and the integrity of the assistance profile. Third, a fundamental frequency estimation based on discrete Fourier transform (DFT) is proposed to shorten the convergence time of EAO significantly. The finite state machine (FSM) is designed to improve the stability and practicality of EAO. Finally, we demonstrate the effectiveness of the prerequisite condition for the CE-based flexion-assisted method by using electromyography (EMG) and metabolic indicators in experiments. In particular, for the knee joint, CE-based flexion assistance should be within an entire joint power period rather than just in the negative power phase. Ensuring the human's active movement will also significantly reduce the activation of antagonistic muscles. This study will aid in designing assistive methods from the perspective of natural human actuation and apply the EAO to the human-exoskeleton system.

Computational Estimates of Pitch Height and Pitch Strength in Dysphonic Voices

<h3>Research Objectives</h3> To evaluate the utility of automated computational estimates of pitch height and pitch strength in characterizing dysphonic voices that have glottal (i.e., true vocal folds) and supraglottal (e.g., false vocal folds), vibratory sources (GVS and SGVS). Furthermore, the utility of such pitch-based measures (Zwicker & Fastl, 1990) in characterizing and differentiating these voice signals that vary in periodicity (Type I, II, and III) was also tested (Titze, 1994). <h3>Design</h3> Repeated measures. <h3>Setting</h3> University. <h3>Participants</h3> Dysphonic voice samples (sustained /a/ and sentence) from 30 adults with GVS (10 per signal type) and 30 adults with SGVS (10 per signal type) were selected from a large database through stratified-random sampling. Pitch height and pitch strength were estimated from Auditory-Sawtooth Waveform Inspired Pitch Estimator Prime (Aud-SWIPE', Camacho, 2012) algorithm and compared with conventional fundamental frequency (f0) estimates from PRAAT software (Boersma, 2022). <h3>Interventions</h3> Not Applicable. <h3>Main Outcome Measures</h3> It is hypothesized that dysphonic voices with SGVS will have lower pitch height and pitch strength than GVS due to the inherent differences in anatomical structures of vibration and their associated physiological properties (Alipour & Karnell, 2014; Schwarz et al., 2011). It is also hypothesized that there will be a significant difference in pitch height and pitch strength between the Type I, II, and III voice signals varying in periodicity (Anand et al., 2021). <h3>Results</h3> Pitch height and pitch strength were higher in GVS compared to SGVS. Estimates of pitch height and f0 from were highly correlated and were in close agreement for Type I signals compared to other signal types where PRAAT was unable to provide f0 trace for some voices. Pitch strength was highest for Type I signals and lowest for Type III signals. <h3>Conclusions</h3> Pitch height and pitch strength can be measured in all dysphonic voices irrespective of signal periodicity. <h3>Author(s) Disclosures</h3> Supraja Anand receives salary from the University of South Florida.

Performance analysis of various fundamental frequency estimation algorithms in the context of pathological speech.

Reliable fundamental frequency (f0) extraction algorithms are crucial in many fields of speech research. The current bulk of studies testing the robustness of different algorithms have focused on healthy speech and/or measurements of sustained vowels. Few studies have tested f0 estimations in the context of pathological speech, and even fewer on continuous speech. The present study evaluated 12 available pitch detection algorithms on a corpus of read speech by 24 speakers (8 healthy speakers, 8 speakers with Parkinson's disease, and 8 with head and neck cancer). Two fusion methods' algorithms have been tested: one based on the median of algorithms and one based on the fusion between the best algorithm for voicing detection and the algorithm that generates the most accurate f0 estimations on voiced parts. Our results show that time-domain algorithms, like REAPER, are best for voicing detection while deep neural network algorithms, like FCN- f0, yield better accuracy for the f0 values on voiced parts. The combination of REAPER and FCN- f0 yields the best ratio performance/implementation complexity, since it generates less than 4% errors on voicing detection and less than 5% of gross errors in the estimation of the f0 values for all speaker groups.

Prediction of Voice Fundamental Frequency and Intensity from Surface Electromyographic Signals of the Face and Neck.

Silent speech interfaces (SSIs) enable speech recognition and synthesis in the absence of an acoustic signal. Yet, the archetypal SSI fails to convey the expressive attributes of prosody such as pitch and loudness, leading to lexical ambiguities. The aim of this study was to determine the efficacy of using surface electromyography (sEMG) as an approach for predicting continuous acoustic estimates of prosody. Ten participants performed a series of vocal tasks including sustained vowels, phrases, and monologues while acoustic data was recorded simultaneously with sEMG activity from muscles of the face and neck. A battery of time-, frequency-, and cepstral-domain features extracted from the sEMG signals were used to train deep regression neural networks to predict fundamental frequency and intensity contours from the acoustic signals. We achieved an average accuracy of 0.01 ST and precision of 0.56 ST for the estimation of fundamental frequency, and an average accuracy of 0.21 dB SPL and precision of 3.25 dB SPL for the estimation of intensity. This work highlights the importance of using sEMG as an alternative means of detecting prosody and shows promise for improving SSIs in future development.

Estimating steelpan note class from attack transients

The estimation of fundamental frequency of instruments is an important task in computational audio analysis. The current state of the art methods use neural networks for this task. This process is typically computed periodically over very short segments of a monophonic audio signal so that minute shifts in intonation can be detected. However, the steelpan has discretely tuned notes where the performer has no direct control over pitch once a note has been activated. The activation of a note has great influence over the acoustical properties of the resultant note. Much research has been devoted to the tonality, construction, and acoustical properties of steelpans, but relatively little focuses on the attack transient specifically.This paper evaluates the application of pitch detection methods to the attack transients of steelpan notes. A dataset containing labeled audio samples from multiple tenor steelpans is used for training and evaluation. The accuracy of this approach for pitch detection is compared with established methods applied to both entire notes and only attack transients. Determining a steelpan note’s pitch from the attack transient is an important first step in building a robust low latency automatic transcription system that can be used for both analysis as well as live performance.

LibACA, pyACA, and ACA-Code: Audio content analysis in 3 languages

The three packages libACA, pyACA, and ACA-Code provide reference implementations for basic approaches and algorithms for the analysis of musical audio signals in three different languages: C++, Python, and Matlab. All three packages cover the same algorithms, such as extraction of low level audio features, fundamental frequency estimation, as well as simple approaches to chord recognition, musical key detection, and onset detection. In addition, it implementations of more generic algorithms useful in audio content analysis such as dynamic time warping and the Viterbi algorithm are provided. The three packages thus provide a practical cross-language and cross-platform reference to students and engineers implementing audio analysis algorithms and enable implementation-focused learning of algorithms for audio content analysis and music information retrieval.

Research on Discourse Transfer Analysis Based on Deep Learning of Cross-language Transfer

With the current exchange and communication between different countries becoming more and more frequent, the language conversion of different countries has become a difficult problem. The analysis of a series of problems in cross-language discourse conversion, the study of the discourse conversion path, and innovation motivation based on the deep learning theory of cross-language transfer, it has theoretical and practical significance. This paper aims at the technical difficulties in speech conversion methods to effectively utilize the local mode information of signal time spectrum and the long-term correlation of speech signal. A discourse conversion method based on convolutional recurrent neural network model is proposed. In the model, the extended convolutional neural network is used to model the long-term correlation of speech signals. In the part of speech fundamental frequency estimation, the prosodic information generated by the decomposition of the fundamental frequency by continuous wavelet transform is used as the training target of the fundamental frequency estimation model. The experimental results show that the speech transformation method based on the convolutional cyclic network model proposed in this paper has better quality and intelligibility than the speech transformed by the contrast method.

Machine Learning Approaches for Whisper to Normal Speech Conversion

Whispered speech is a mode of speech that differs from normal speech due to the absence of a periodic component, namely the Fundamental Frequency that characterizes the pitch, among other spectral and temporal differences. Much attention has been given in recent years to the application of Machine Learning techniques for voice conversion tasks. The whisper-to-normal speech conversion is particularly challenging, however, especially with respect to the Fundamental Frequency estimation. Based on the most recent literature, this survey assesses the state-of-the-art regarding Machine Learning based whisper-to-normal speech conversion, identifying trends both on modeling and training approaches. The proposed solutions include Generative Adversarial Network based, Autoencoder based and Bidirectional Long Short-Term Memory based frameworks, among other Deep Neural Network based architectures. In addition to Parallel versus Non-Parallel training, time-alignment requirements and strategies, datasets, vocoder usage, as well as both objective and subjective evaluation metrics are also covered by the present survey.

An enhanced fast fundamental frequency estimator for three-phase electric aircraft grid

This article proposes a robust and enhanced three-phase fundamental frequency estimation algorithm for the electric aircraft grid. Unlike conventional frequency-locked loops, the digital signal processing technique-based frequency estimator proposed relies on the storage of five consecutive samples of the fundamental grid voltage signal. Furthermore, the ability to successfully operate at a low sampling frequency, i.e. 8 kHz, makes it sufficiently attractive as regards reducing the memory storage in a low-cost real-time controller. The proposed frequency estimator can additionally eliminate the negative effects of the DC-offset and the fundamental negative sequence components present in the grid signal without any additional effort. Also, the tuning efforts are reduced for the frequency variation range of 350–900 Hz owing to the existence of a single tuning gain parameter. The proposed algorithm has also been found to have a fast dynamic response, which has been experimentally validated through the use of a real-time digital controller.

A New Set of Automated Methodologies for Estimating Site Fundamental Frequency and Its Uncertainty Using Horizontal-to-Vertical Spectral Ratio Curves

AbstractThis study proposes a new set of methodologies to estimate the site fundamental frequency using the horizontal-to-vertical spectral ratio (HVSR) of recorded surface ground motions. Because of the lack of consensus in HVSR calculation among researchers, a wide range of methods are practiced in this area, yielding different site fundamental frequencies at a given site due to analyst subjectivity. In this study, current practices for combining horizontal components—geometric mean and RotD50—are examined first, and results show that both methods provide comparable HVSR curves. However, RotD50 has the advantage of being orientation independent. Second, the application of Fourier amplitude spectrum (FAS) and 5% damped pseudospectral acceleration (PSA) in computing HVSR is studied, and results are presented for one case study in which PSA-based HVSR seems to suffer from scenario dependency, whereas the FAS-based results appear stable. Different values for Konno–Ohmachi smoothing parameter b were evaluated, and its effect on estimating the site fundamental frequency was considered; using b = 40 is our preference. In previous studies, average HVSR curves were used to estimate a single number representing the site fundamental frequency without incorporating uncertainty. This study proposes four methodologies that use events’ individual HVSR curves to estimate the site fundamental frequency and its associated uncertainty in a completely automated manner. Methods 1–3 use individual HVSR curves to find the maximum-likelihood estimate of the site fundamental frequency (fml), whereas method 4 uses both individual and average HVSR curves to estimate the first resonance frequency (f0). To evaluate the automated methods, a subset of the Next Generation Attenuation-West2 dataset is used to study 50 stations, and the results are compared with an independent study demonstrating good consistency. The proposed methods are further illustrated using data from the Garner Valley Downhole Array (GVDA), which highlights the pros and cons of the presented methods.

Fundamental frequency estimation by an interpolated DFT algorithm eliminating negative-image component interference in arbitrary windows

Interpolated discrete Fourier transform (IpDFT) is an effective algorithm for spectrum analysis. However, the interference effect from the negative-image component significantly influences the accuracy of spectrum analysis for a small number of acquired sine wave cycles. In this study, a high-accuracy IpDFT algorithm is proposed for fundamental frequency estimation, wherein the interference effect of the fundamental negative-image component is theoretically eliminated. The proposed IpDFT algorithm uses the real or imaginary parts of three DFT bins with the largest amplitudes to establish the interpolation formula, which is employed to correct the frequency deviation caused by the picket fence effect. Additionally, this algorithm is suitable for arbitrary windows. The calculation process is simplified using the lookup-table method. Moreover, the effectiveness of the proposed IpDFT algorithm is verified by simulation and experimental results. The frequency estimation accuracy of the proposed IpDFT algorithm is comparatively analyzed with those of several state-of-the-art IpDFT algorithms for both noisy and noisy-and-harmonically distorted sine waves.

Noisy Speech Based Temporal Decomposition to Improve Fundamental Frequency Estimation

This paper introduces a novel method to separate voiced frames of noisy speech signals into low-frequency or high-frequency. This separation improves the accuracy of fundamental frequency (F0) estimators. In this proposal, the target signal is analyzed by means of the ensemble empirical mode decomposition. Next, the pitch information is extracted from the first decomposition modes. This feature indicates the frequency region where the speech F0 should be located, thus separating the frames into low-frequency or high-frequency. The frames separation is then applied to correct pitch candidates extracted from a F0 detection method, improving the estimation accuracy. The proposed method and a baseline separation approach are evaluated considering four different F0 estimation algorithms. Experiments are conducted with the CSTR and TIMIT databases, and six noises with various signal-to-noise ratios. The Gross Error (GE) and Mean Absolute Error (MAE) metrics are adopted to evaluate the solutions in terms of F0 estimation errors. Results show that the proposed method outperforms the baseline, in terms of low/high frequency separation accuracy. Moreover, the novel solution is able to better improve F0 detection accuracy under different noisy conditions.

Instantaneous Fundamental Frequency and Model Order Estimation of Non-Stationary Harmonic Signals

Instantaneous Fundamental Frequency and Model Order Estimation of Non-Stationary Harmonic Signals