Fundamental Frequency Distribution Research Articles

The fundamental frequency (f0) distribution of American speakers in a spontaneous speech corpus*

The fundamental frequency (f0) distribution of American speakers in a spontaneous speech corpus*

The potential of spatial statistics for the reconstruction of a subsoil model: A case study for the Firenze-Prato-Pistoia Basin, Central Italy

A reliable subsoil model represents the first step in assessing potential geological hazards and adopting proper mitigation measures accordingly. However, one of the main difficulties related to the definition of such models concerns the extrapolation of single-point data over wide, uninvestigated areas. For this reason, in this work, we reconstruct a subsoil model within an alluvial basin through a methodology specifically based on spatial-statistical analyses of geophysical in situ point measurements. In particular, measurements of ambient noise were analysed and extrapolated to obtain a spatially continuous distribution of fundamental resonance frequency (f0) over the entire basin. Local portions of the basin were then defined according to a specific relationship between f0 and the minimum distance from the bedrock outcrops (MDBO). This analysis revealed how the position of the identified clusters is consistent with the asymmetric geometry of the basin. The resulting simplified subsoil model was then validated through additional experimental measurements of ambient noise to evaluate the reliability of the proposed methodology. As the test site, we selected the Firenze-Prato-Pistoia Basin (Tuscany region, central Italy), where more than two hundred homogeneously distributed noise measurements were collected from previous seismic microzonation investigations.

Effects of speaking style on the shape of fundamental frequency distributions

The present study has two main goals. The first is to describe the effects of three speaking styles (spontaneous interview, sentence reading and word list reading) on statistical estimators of fundamental frequency (f0) variability (mean, standard deviation, skewness and kurtosis) in five female and five male speakers of Brazilian Portuguese (BP). Most f0 contours of word reading are bimodal. Analysis of their time-normalized contours suggests this is caused by the time-compressed realization of fast transitions from low to high or high to low tones aligned with stressed syllables. Considering only unimodal distributions, results show that there are no statistically significant effects in the male data for any of the four variability estimators. Effects show up in female data. Spontaneous style has statistically significant higher mean, SD and skewness than read speech. Findings in the previous literature indicate the reverse pattern, though, for languages other than BP. The second goal of the study is to characterize the statistical properties of f0 distributions beyond mean and SD. Results confirm previous observations that most f0 distributions have positive skewness, are left-tailed and have kurtosis values that deviate significantly from the normal because of large deviations from the central or modal value. A distribution fitting procedure tested six distributions. The asymmetric Burr type XII distribution emerges as the one that best fits the data in the corpus. Results show that two of the parameters that determine its shape correlate well with the empirical f0 distribution values of SD and skewness. Important effects of speaking style on f0 seen in female speakers can be reproduced by combinations of the Burr distributions’ parameters.

Estimation of the Site Effect Using Microtremor Technique at New Akhmim City, Akhmim, Sohag, Egypt

Abstract —Local site effect is a significant aspect of seismic hazards, which often causes amplification of ground motions and results in increase in the damage potential of an earthquake. This article displays an experimental study of microtremors data to investigate the dynamic characteristics of the soil and structures in the desert zone of Akhmim City, east of River Nile, Sohag governorate, Egypt. Because of progressive population growth in the Nile valley and delta regions, the Egyptian Governorate considered increasing the number of new communities, especially in the Sohag district, to improve the living conditions. The study area is one of the new urban areas which was suggested by Egyptian Urban Communities Authority (EUCA). For this purpose, the horizontal to vertical (H/V) spectral ratio was used to provide precious information about the soil properties and its engineering features for foundation purposes. The H/V spectral ratio analyses of ambient noise data at the measurement stations were processed and interpreted using Geopsy Software to calculate the amplification factor and fundamental resonance frequency at each observation point. The results indicate that the resonance frequency ranges between 0.21 and 0.28 Hz at the most of the measurement stations, with some irregularities at stations No. 2 and 4 because of the higher softness of sediments in these locations. Most of lower fundamental frequencies are observed in the southern part of the study area, whereas higher values are observed in the northern part of the study area. The amplification factor ranges between 1.38 and 4.15. Higher values were recorded in the northeastern and southern parts, while lower ones were observed in the northwestern and southwestern parts of the mapped area. It can be concluded that the amplification component increases with increasing softness of the sediments. Interpretation of fundamental frequency distribution map is very significant to estimate the building heights and the number of stories, which was estimated to be 35 to 47.

Influence of tests results on serial production of EXFEL superconducting cavities

The European XFEL (EXFEL) 1.3 GHz cavities were produced without any final cold RF performance guarantee for characteristics like accelerating gradient, quality factor or field emission. In the case of low-performance, DESY provided all re-treatment procedures in order to improve these characteristics getting closer to specification levels. But EXFEL cavities have very tight tolerances for the parameters like cavity length, cells eccentricity, fundamental mode frequency and field distribution on the operational mode. Usage of modern infrastructure, analytical methods and powerful tools of the database analysis allows us not only keeping these characteristics in specified ranges, but also investigate the cavity shape uncertainties and improve the damping of the higher order modes.

Cognitive Load in Voice Therapy Carry-Over Exercises.

The cognitive load generated by online speech production may vary with the nature of the speech task. This article examines 3 speech tasks used in voice therapy carry-over exercises, in which a patient is required to adopt and automatize new voice behaviors, ultimately in daily spontaneous communication. Twelve subjects produced speech in 3 conditions: rote speech (weekdays), sentences in a set form, and semispontaneous speech. Subjects simultaneously performed a secondary visual discrimination task for which response times were measured. On completion of each speech task, subjects rated their experience on a questionnaire. Response times from the secondary, visual task were found to be shortest for the rote speech, longer for the semispontaneous speech, and longest for the sentences within the set framework. Principal components derived from the subjective ratings were found to be linked to response times on the secondary visual task. Acoustic measures reflecting fundamental frequency distribution and vocal fold compression varied across the speech tasks. The results indicate that consideration should be given to the selection of speech tasks during the process leading to automation of revised speech behavior and that self-reports may be a reliable index of cognitive load.

An analysis of music sound by a 12 even-tempered discrete wavelet

Music sounds are analyzed using a 12 even-tempered wavelet based upon the variable-density perfect translation invariance complex discrete wavelet transform (VD-PTI-CDWT) which divides an octave frequency band into 12 filter banks of equivalent width. Music chords generated from different sound sources thus analyzed are represented as scalogram and in 3 dimension (3D) graph over time-frequency domain. The scalogram representation provides information corresponding to the western music notation and accords with human's cognition for pitch of the music sound whereas 3D graph representation is capable of providing more detail sound information. We further apply the method to Specmurt analysis in order to estimate the fundamental frequency distribution of polyphonic music sound. The polyphonic sound of C 4, G 4, D 5, A 5 in scientific notation generated with saw-tooth wave tone is successfully filtered out its overtones to provide the fundamental frequency distribution.

Effects of driving frequency of longitudinal transducer on the vibration characteristics of a stepped plate

The flexural vibration characteristics of a stepped plate, driven at its center by different frequency of longitudinal transducer with a certain area are investigated. The variation in the nodal circle, fundamental frequency and displacement distribution of the stepped plate are calculated by using finite element method (FEM) under different driving frequencies. The results show that the fundamental frequency and nodal circle of the flexural-vibration stepped plate (FVSP) increase with an increase in the driving frequency of the longitudinal vibration ultrasonic transducer (LVUT), before the second-order flexural vibration occurs. When the driving frequency is f=28kHz, the displacement amplitude of the stepped plate can achieve the maximum, and the nodal circle radius of the stepped plate is 2.61cm which fits evenly the edge of stepped profile. Meanwhile, the directivity and radiation efficiency of the FVSP would be greatly improved in a special driving frequency. The conclusions agree with the experimental ones and are significant for both design and applications of the stepped plate.

Gender Categorization in Cochlear Implant Users

In this study, the authors examined the ability of subjects with cochlear implants (CIs) to discriminate voice gender and how this ability evolved as a function of CI experience. The authors presented a continuum of voice samples created by voice morphing, with 9 intermediate acoustic parameter steps between a typical male and a typical female. This method allowed for the evaluation of gender categorization not only when acoustical features were specific to gender but also for more ambiguous cases, when fundamental frequency or formant distribution were located between typical values. Results showed a global, though variable, deficit for voice gender categorization in CI recipients compared with subjects with normal hearing. This deficit was stronger for ambiguous stimuli in the voice continuum: Average performance scores for CI users were 58% lower than average scores for subjects with normal hearing in cases of ambiguous stimuli and 19% lower for typical male and female voices. The authors found no significant improvement in voice gender categorization with CI experience. These results emphasize the dissociation between recovery of speech recognition and voice feature perception after cochlear implantation. This large and durable deficit may be related to spectral and temporal degradation induced by CI sound coding, or it may be related to central voice processing deficits.

Mixed Music Analysis with Extended Specmurt

This paper introduces a mixed music analysis method using extended specmurt analysis. Conventional specmurt can only analyze a multi-pitch music signal from a single instrument and cannot analyze a mixed music signal that has several different types of instruments being played at the same time. To analyze a mixed music signal, extended specmurt is proposed. We regard the observed spectrum extracted from the mixed music as the summation of the observed spectra corresponding to each instrument. The mixed music has as many unknown fundamental frequency distributions as the number of instruments since the observed spectrum of a single instrument can be expressed as a convolution of the common harmonic structure and the fundamental frequency distribution. The relation among the observed spectrum, the common harmonic structure and the fundamental frequency distribution is transformed into a matrix representation in order to obtain the unknown fundamental frequency distributions. The equation is called extended specmurt, and the matrix of unknown components can be obtained by using a pseudo inverse matrix. The experimental result shows the effectiveness of the proposed method.

Sparseness Criteria of F0-Frequencies Selection for Specmurt-Based Multi-Pitch Analysis without Modeling Harmonic Structure

This paper introduces a multi-pitch analysis method using specmurt analysis without modeling the common harmonic structure pattern. Specmurt analysis is based on the idea that the fundamental frequency distribution is expressed as a deconvolution of the observed spectrum by the common harmonic structure pattern. To analyze the fundamental frequency distribution, the common harmonic structure needs to be modeled accurately because it is often unknown while the observed spectrum is known. It is considered impossible, however, to obtain a highly accurate model of the structure since it can vary slightly depending on the pitch. Therefore we propose a method to analyze the fundamental frequency distribution without modeling the harmonic structure. We note that each peak of the observed spectrum indicates the fundamental frequency or the harmonic tone. Hence, the fundamental frequency distribution can be regarded as the set which only has the peaks corresponding to fundamental frequencies. To find the set, we prepare many sets of the peaks of the spectrum, and obtain a large number of common harmonic structures. We evaluate the sparseness of these structures using L1 or L2 norm, and then select the set that has derived the sparsest structure as a solution. The experimental result shows the effectiveness of the proposed method.

Local Site Response in an Alpine Valley from Recorded Earthquakes and Ambient Noise Analysis

Local response is estimated within the sediment fill of the Tagliamento River Valley (THV), northeastern Italy, using about 90 weak‐to‐medium local and regional earthquakes. Ground motion is recorded at six stations deployed in a linear array across the valley. Site amplification factors are determined using the standard spectral ratio, the generalized inversion technique, and evaluations of receiver functions. Results obtained from earthquake data are then compared with ambient noise analysis. Azimuthal effects in the seismic response are observed locally for waves coming from the east‐southeast, aligned with the longitudinal axis of the valley. The seismic responses evaluated at the mid‐valley and at the valley edge are then convolved with the 1976 M w 6.4 Friuli mainshock recorded at accelerometric station TLM1, located close to the array. The local response at the valley edge, in the town of Cavazzo Carnico, is responsible for an enhancement of the input motion of an average factor of about 4 in the frequency range from 2 to 8 Hz. The elastic demand from the current national regulation for a 475‐year return period and specific for Cavazzo Carnico is overcome by the 5%‐damped pseudoacceleration response spectrum estimated at the valley edge. The underestimation of the Italian code is mostly due to a 2D amplification effect at the valley edge rather than a simple inadequacy of the V S 30 site classification. Online Material: Figures showing locations of historical earthquakes, distribution of fundamental frequency of vibration, waveforms of the M D 5.1 Kobarid earthquake, S ‐wave velocity versus depth, and GIT and RF amplification median values and spectra; tables of seismic station locations and soil type, and of local and regional earthquakes.

Acoustical study of classical Peking opera singing

Acoustic characteristics of classical opera singing differ considerably between the Western and the Chinese cultures. Singers in the classical Peking opera tradition are specializing on one out of a limited number of standard roles. Audio and electroglottograph signals were recorded of four performers of the Old Man roel and four performers of the Colorful Face role. Recordings were made of the singers' speech and when they sang recitatives and songs from their repertoires. Sound pressure level, fundamental frequency and spectrum characteristics were analyzed. Histograms showing the distribution of fundamental frequency showed marked peaks for the songs, suggesting a scale tone structure. Some of the intervals between these peaks were similar to those used in Western music. Vibrato rate was about 3.5 Hz, i.e., considerably slower than in Western classical singing. Spectra of vibrato-free tones contained unbroken series of harmonic partials sometimes reaching up to 17000 Hz. LTAS curves showed no trace of a singer's formant cluster. However, the Colourful Face role singers' LTAS showed a marked peak near 3300 Hz, somewhat similar to that found in Western pop music singers. The mean LTAS slope between 700 and 6000 Hz decreased by about 3 dB/octave per dB of equivalent sound level.

A Mixed Quantum-Classical Molecular Dynamics Study of the Hydroxyl Stretch in Methanol/Carbon Tetrachloride Mixtures: Equilibrium Hydrogen-Bond Structure and Dynamics at the Ground State and the Infrared Absorption Spectrum

We present a mixed quantum-classical molecular dynamics study of the structure and dynamics of the hydroxyl stretch in methanol/carbon tetrachloride mixtures. One of the methanol molecules is tagged, and its hydroxyl stretch is treated quantum-mechanically, while the remaining degrees of freedom are treated classically. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the corresponding adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are in turn affected by the quantum-mechanical state of the tagged hydroxyl stretch via the corresponding Hellmann-Feynman forces. The ability of five different force-field combinations to reproduce the experimental absorption infrared spectrum of the hydroxyl stretch is examined for different isotopomers and on a wide range of compositions. It is found that, in addition to accounting for the anharmonic nature of the hydroxyl stretch, one also has to employ polarizable force fields and account for the damping of the polarizability at short distances. The equilibrium ground-state hydrogen-bonding structure and dynamics is analyzed, and its signature on the absorption infrared spectrum of the hydroxyl stretch is investigated in detail. Five different hydroxyl stretch subpopulations are identified and spectrally assigned: monomers (α), hydrogen-bond acceptors (β), hydrogen-bond donors (γ), simultaneous hydrogen-bond donors and acceptors (δ), and simultaneous hydrogen-bond donors and double-acceptors (ε). The fundamental transition frequencies of the α and β subpopulations are found to be narrowly distributed and to overlap, thereby giving rise to a single narrow band whose intensity is significantly diminished by rotational relaxation. The fundamental transition frequency distributions of the γ, δ, and ε subpopulations are found to be broader and to partially overlap, thereby giving rise to a single broad band which is red-shifted relative to the αβ band. The γδε band is also found to be inhomogeneously broadened and unaffected by rotational relaxation. The exchange rates between the different subpopulations and corresponding branching ratios are reported and explained. Finally, nonlinear mapping relations between the hydroxyl transition frequency and bond length and the electric field along the hydroxyl bond axis are established, which can be used to reduce the computational cost of the mixed quantum-classical treatment to that of a purely classical molecular dynamics simulation.

Acoustical Study of Classical Peking Opera Singing

Acoustic characteristics of classical opera singing differ considerably between the Western and the Chinese cultures. Singers in the classical Peking opera tradition specialize on one out of a limited number of standard roles. Audio and electroglottograph signals were recorded for four performers of the Old Man role and three performers of the Colorful Face role. Recordings were made of the singers' speech and when they sang recitatives and songs from their roles. Sound pressure level, fundamental frequency, and spectrum characteristics were analyzed. Histograms showing the distribution of fundamental frequency showed marked peaks for the songs, suggesting a scale tone structure. Some of the intervals between these peaks were similar to those used in Western music. Vibrato rate was about 3.5Hz, that is, considerably slower than in Western classical singing. Spectra of vibrato-free tones contained unbroken series of harmonic partials sometimes reaching up to 17000Hz. Long-term-average spectrum (LTAS) curves showed no trace of a singer's formant cluster. However, the Colorful Face role singers' LTAS showed a marked peak near 3300Hz, somewhat similar to that found in Western pop music singers. The mean LTAS spectrum slope between 700 and 6000Hz decreased by about 0.2dB/octave per dB of equivalent sound level.

Multipitch analysis with specmurt based on the sparseness of the common harmonic structure pattern.

A novel multipitch analysis based on specmurt with the sparseness of the common harmonic structure pattern is presented. The conventional specmurt analysis is based on the idea that a fundamental frequency distribution is expressed as a deconvolution of the observed spectrum by the common harmonic structure pattern. However, it is considered impossible to obtain the strictly correct model of the common harmonic structure since harmonic structures can slightly vary depending on the pitch. Therefore a new method to analyze the fundamental frequency distribution without modeling the common harmonic structure is proposed. In this method, many possible fundamental frequencies are prepared using observed spectrum peaks, and harmonic and nonharmonic structures corresponding to them are obtained by the deconvolution of observed spectrum. Then, based on the sparseness, L1 or L2 norms are applied to only the appropriate harmonic structures in order to obtain a correct harmonic structure. The experimental result shows the effectiveness of our proposed method.

Site characterization by seismic noise in Istanbul, Turkey

Single station seismic noise measurements were carried out at 192 sites in the western part of Istanbul, Turkey. This extensive survey allowed the fundamental resonance frequency of the sedimentary cover to be mapped, and identify areas prone to site amplification. The results are in good agreement with the geological distribution of sedimentary units, indicating a progressive decrease of the fundamental resonance frequencies from the northeastern part, where the bedrock outcrops, towards the southwestern side, where a thickness of some hundreds meters for the sedimentary cover is estimated. The particular distribution of fundamental resonance frequencies indicates that local amplification of the ground motion might play a significative role in explaining the anomalous damage distribution after the 17 August 1999 Kocaeli Earthquake. Furthermore, 2D array measurements of seismic noise were performed in the metropolitan area with the aim of obtaining a preliminary geophysical characterization of the different sedimentary covers. These measurements allow the estimation of the shear-wave velocity profile for some representative areas and the identification of the presence of strong impedance contrast responsible of seismic ground motion amplification. Comparison of a theoretical site response from an estimated S-wave velocity profile with an empirical one based on earthquake recordings strongly encourages the use of the low cost seismic noise techniques for the study of seismic site effects.

Specmurt Analysis of Polyphonic Music Signals

This paper introduces a new music signal processing method to extract multiple fundamental frequencies, which we call specmurt analysis. In contrast with cepstrum which is the inverse Fourier transform of log-scaled power spectrum with linear frequency, specmurt is defined as the inverse Fourier transform of linear power spectrum with log-scaled frequency. Assuming that all tones in a polyphonic sound have a common harmonic pattern, the sound spectrum can be regarded as a sum of linearly stretched common harmonic structures along frequency. In the log-frequency domain, it is formulated as the convolution of a common harmonic structure and the distribution density of the fundamental frequencies of multiple tones. The fundamental frequency distribution can be found by deconvolving the observed spectrum with the assumed common harmonic structure, where the common harmonic structure is given heuristically or quasi-optimized with an iterative algorithm. The efficiency of specmurt analysis is experimentally demonstrated through generation of a piano-roll-like display from a polyphonic music signal and automatic sound-to-MIDI conversion. Multipitch estimation accuracy is evaluated over several polyphonic music signals and compared with manually annotated MIDI data.

Modeling prosodic differences for speaker recognition

Prosody plays an important role in discriminating speakers. Due to the complexity of estimating relevant prosodic information, most recognition systems rely on the notion that the statistics of the fundamental frequency (as a proxy for pitch) and speech energy (as a proxy for loudness/stress) distributions can be used to capture prosodic differences between speakers. However, this simplistic notion disregards the temporal aspects and the relationship between prosodic features that determine certain phenomena, such as intonation and stress. We propose an alternative approach that exploits the dynamics between the fundamental frequency and speech energy to capture prosodic differences. The aim is to characterize different intonation, stress, or rhythm patterns produced by the variation in the fundamental frequency and speech energy contours. In our approach, the continuous speech signal is converted into a sequence of discrete units that describe the signal in terms of dynamics of the fundamental frequency and energy contours. Using simple statistical models, we show that the statistical dependency between such discrete units can capture speaker-specific information. On the extended-data speaker detection task of the 2001 and 2003 NIST Speaker Recognition Evaluation, such approach achieves a relative improvement of at least 17% over a system based on the distribution statistics of fundamental frequency, speech energy and their deltas. We also show that they are more robust to communication channel effects than the state-of-the-art speaker recognition system. Since conventional speaker recognition systems do not fully incorporate different levels of information, we show that the prosodic features provide complementary information to conventional systems by fusing the prosodic systems with the state-of-the-art system. The relative performance improvement over the state-of-the-art system is about 42% and 12% for the extended-data task of the 2001 and 2003 NIST Speaker Recognition Evaluation, respectively.

Inverse filter analysis of common harmonic structure on Specmurt using Riemann’s ζ function

In this paper, based on the interesting relationship between the log‐spaced δ function sequence and Riemann’s ζ function, the analytical properties of the inverse filter of the common harmonic structure on specmurt analysis are discussed. Specmurt [S. Sagayama et. al., in Proc. SAPA (2004)] is a simple and efficient technique for the multi‐pitch analysis of polyphonic music signals. If all tones have the same harmonic pattern, the power spectrum on the log‐scaled frequency can be regarded as the convolution of the common harmonic structure and the distribution of fundamental frequencies. Based on the model, overtones are effectively suppressed by the inverse filtering of the common harmonic structure in specmurt. Thus, for the stable processing, analytic properties of the inverse filter are significant. Our new finding is that when the common harmonic structure is expressed as a log‐spaced δ function sequence with a particular kind of decay, the Fourier transform is exactly equal to Riemann’s ζ function. Interpreting several properties of Riemann’s ζ function in a signal processing context gives us the new perspectives like an explicit representation or cascaded decomposition of the inverse filter.