Determination Of Fundamental Frequency Research Articles

Adaptive determination of fundamental frequency for direct time-domain averaging

Time-domain averaging (TDA), as an effective signal processing technique for periodic signal enhancement has been widely used for fault detection of gearboxes and bearings. TDA normally requires a tachometer signal to provide an accurate estimation of fundamental frequency. However, tachometer is unavailable or difficult to use in many applications. In this paper, an adaptive fundamental-frequency determination method without tachometer signal is proposed. Firstly, the effect of fundamental-frequency estimation error on direct TDA is investigated, and it indicates that minor error of estimation can cause severe deterioration in curve of attenuation coefficient. Secondly, harmonic-to-noise ratio (HNR) is proposed to evaluate the result of direct TDA for a given fundamental frequency, and it is utilized to optimize the fundamental frequency from a number of candidates. Finally, average waveform is obtained by implementing direct TDA with the optimized fundamental frequency. Examples of gear faults are given to verify the proposed method. The derived fundamental frequency is accurate, and average waveforms indicate the presence of gear faults successfully.

Classification of the fundamental frequency identification methods

A significant role in the formation of the voice characteristics of the information signals given to the speaker system represents a language group, which is responsible for basic voice parameters such as pitch frequency of the signal, information frames and properties frequency range, volume, frequency and rate of speech, intonation, etc. The main criteria features of voice were identified. The basic characteristics of audio signals generated by a person of a certain language group were analyzed. The methods and models to identify the fundamental frequency, which further gave the opportunity to determine the period of the fundamental tone were analyzed. In the current research, the determination of the fundamental frequency, there are problems such as the complexity of the implementation methods, and low probability of error in determination process; low resistance methods to external interference. Methods of determination of fundamental frequency with the plane of their implementation were classified.

Soil-structure interaction at railway bridges with integral abutments

An Austrian composite single span bridge with integral abutments has been measured at different construction levels to investigate the contribution of backfill behind abutments on static and dynamic properties of the soil-structure system and their differences. Especially the determination of fundamental frequencies and corresponding damping ratios is of high interest. This paper describes the structural characteristics of the investigated bridge and the conducted measurements. As first results, the fundamental frequencies obtained at the different construction levels are presented and discussed.

Determination of Fundamental Frequency and Voice Intensity in Iranian Men and Women Aged Between 18 and 45 Years

Acoustic measurements have become an essential aspect of voice assessment during the last few decades, and studies have established that normative data is necessary for acoustic analysis. In this study, two aspects of voice are reviewed. These two factors are fundamental frequency and intensity. This study was designed to establish the normal acoustic analysis parameters in normal Iranian adults. In this cross-sectional study, 200 healthy randomly selected subjects (100 men and 100 women) were assessed. Data collection was carried out using the Studio Speech software and Laryngograph processor (Laryngograph Ltd, London, UK), type: PCLX at the Larynx and Voice Disorders Clinic of Rasoul-e-Akram Hospital under comfortable phonation. The value of fundamental frequency in reading was greater for women (170-240 Hz) than for men (107-140 Hz). Also, the value of intensity was greater for women (73.54-84.99 dB) than for men (72.40-86.03 dB). The present study developed the normal data for fundamental frequency and intensity in Iranian speakers aged between 18 and 45 years. We concluded, fundamental frequency has significant differences between men and women, but intensity has no significant difference between them.

Fundamental frequency estimation of voice of patients with laryngeal disorders

The present paper is aimed at the development of new methods of fundamental frequency determination of voiced signal, uttered by patients with severe laryngeal disorders due to various diseases. The necessity to seek new methods is set by the increasing use of acoustic voice analysis as non-invasive technique for supporting diagnosis in laryngeal pathology. The classic methods, which do not take into account the peculiarities of the pathological voice, do not lead to satisfactory results in case of severely distorted periodicity of the signal. Three new methods are proposed in this paper for fundamental frequency determination: autocorrelation method, spectral method, and cepstral method. Comparison with the most commonly used methods is made.

Fundamental frequency estimation using signal embedding in state space

A new robust nonlinear method for determination of fundamental frequency (F0) was recently proposed with application to speech pitch detection [Terez, Proc. ICASSP 1, 345–348 (2002)]. The method uses state-space embedding technique originally introduced for analyzing chaotic signals. The new method has been generalized and tested on different types of speech signals, as well as on a variety of other acoustic signals. In addition, some artificially generated nonstationary and complex wave forms have been used to test the limits of the method in comparison with other known (short-term) F0-estimation techniques (e.g., correlation, spectrum or cepstrum-based methods). Evaluation results demonstrate a unique combination of properties distinguishing the new method from conventional techniques. In particular, reliable and accurate F0 estimates can be obtained for clean periodic signals using signal segments slightly longer than one complete fundamental period. Other properties include immunity to speech formants and robust performance on noisy and band-limited speech signals. Some improvements are introduced to reduce the number of required computations and to achieve higher (subsample) accuracy. The method waused to implement a robust pitch-tracking algorithm for speech processing applications. Further information and demo software can be found at http://www.soundmathtech.com/pitch.

Determination of fundamental frequency of a physical oscillator by the period fitting method

A period fitting method, which is a variant of the classical least-square fitting method, is proposed to determine the fundamental frequency of a physical oscillator. The root mean square deviation used as the criterion in this method is a single-parameter function of the fundamental frequency of the oscillator, so it makes the fitting process optimize the period fit at the expense of a lesser evaluation of the other parameters such as the amplitude and the phase. Theoretical analysis shows that this method is intrinsically independent of the disturbances of the high order harmonic frequencies oscillation, and the computer simulation experiments show that it is effective to overcome the disturbances of the finite quality factor and the monotonic drift of an oscillator system, as well as the white noise, and this method can determine the fundamental frequency or period of a physical oscillator with a relative precision of 10−7 orders.

Frequency ratios of spectral components of musical sounds

A recently developed high resolution frequency tracker [J. C. Brown and M. S. Puckette, ‘‘A high resolution fundamental frequency determination based on phase changes of the fourier transform,’’ J. Acoust. Soc. Am. 94, 662–667 (1993)] has made it possible to measure the ratios of the frequencies of the upper harmonics of a sound with respect to its fundamental frequency with high accuracy. Calculations were carried out on digitized sounds produced by a clarinet, alto flute, voice, piano, violin, viola, and cello. The sounds produced by the stringed instruments included examples played pizzicato and bowed both with and without vibrato. Measured ratios were exactly equal to integers for all instruments except the piano and strings played pizzicato. Anomalous behavior was observed for the fundamental frequency for vibrato sounds played by stringed instruments with the frequency deviation exceeding the extrema of the other harmonics divided by their harmonic number by about 1% on average. Piano inharmonicity was proportional to harmonic number squared in agreement with Fletcher [J. Acoust. Soc. Am. 36, 203–209 (1964)]. The major limitation on this calculation was found to be instrumental fluctuations.

Fundamental frequency determination based on instantaneous frequency estimation

For certain types of speech coding algorithms, it is important to determine accurately the pitch period or the fundamental frequency of the speech signals. A new fundamental frequency determination method based on the instantaneous frequency estimation is presented in this paper. A bank of two bandpass filters is used to eliminate and attenuate the harmonics of the speech signals. The fundamental frequency can be determined from the estimated instantaneous frequencies of the filtered speech signals. This new method can be used to obtain a continuous fundamental frequency as a function of time. Also, it does not seem to have the problem of occasional incorrect frequency estimation, such as frequency doubling or halving.

Precise determination of fundamental frequency by utilizing harmonic structure of speech

Precise and correct measurement of fundamental frequency F0 is requested in the detailed analysis of speech sound and analysis synthesis telephony employing F0. This paper proposes a new method to estimate F0 employing the harmonic number and its frequency. At first, 256 pts. of speech samples are windowed and ‘‘0’’s are added to 1024 pts. The magnitude spectrum is calculated by FFT and smoothing is carried out by moving average of 5 pts. Such procedures make it easy to identify the spectrum peaks and improve the accuracy of their frequency. Every harmonic is identified from the peak of the spectrum and an harmonic number is assigned. Now fundamental frequency is calculated by (nth) harmonic frequency)/n. Finally the fundamental frequency is computed as the weighted mean, which is proportional to n, on harmonics located under 2 kHz. This idea is quite similar to getting F0 as the coefficient of a regression line passing through the origin. The accuracy of F0 obtained by this method is expected to be less than 3 Hz in female voice when the sampling frequency is 10 kHz. Experimental results indicate that the proposed method gives more precise and reasonable pitch information than the cepstrum or correlation method does.

A high resolution fundamental frequency determination based on phase changes of the Fourier transform

The constant Q transform described recently [J. C. Brown and M. S. Puckette, ‘‘An efficient algorithm for the calculation of a constant Q transform,’’ J. Acoust. Soc. Am. 92, 2698–2701 (1992)] has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages. For this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant Q for lower frequency bins. This modified calculation serves as the input for a fundamental frequency tracker similar to that described by Brown [J. C. Brown, ‘‘Musical fundamental frequency tracking using a pattern recognition method,’’ J. Acoust. Soc. Am. 92, 1394–1402 (1992)]. Once the fast Fourier transform (FFT) bin corresponding to the fundamental frequency is chosen by the frequency tracker, an approximation is used for the phase change in the FFT for a time advance of one sample to obtain an extremely precise value for this frequency. Graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous.

Fundamental frequency determination of speech and singing voice−A review

Fundamental frequency determination methods and algorithms (PDAs) can be grouped into two major classes: time-domain PDAs and short-term analysis PDAs. The short-term analysis PDAs leave the signal domain by a short-term transformation. They supply a sequence of average fundamental frequency estimates from consecutive frames. The individual algorithm is characterized by the short-term transform it applies: autocorrelation, distance functions (average magnitude difference function), least-squares method, harmonic analysis, and multiple spectral transform (cepstrum) are the most common algorithms. The time-domain methods, on the other hand, track the signal period by period. Extraction and isolation of the fundamental harmonic, and investigation of the temporal signal structure are the two extremes between which most of these PDAs are found. Special attention is given to the time-variant aspect of frequency determination and to postprocessing methods that allow fundamental frequency tracking over time. Among these, simple smoothing and list correction procedures are found that remove isolated errors as well as sophisticated schemes that apply dynamic optimization or stochastic modeling.

Fundamental frequency tracking in the log frequency domain based on a pattern recognition algorithm

When the Fourier components of a sound with harmonic frequency components are plotted against log frequency, a constant pattern independent of fundamental frequency is obtained. A computationally efficient implementation [J. C. Brown and M. S. Puckette, ‘‘An efficient algorithm for the calculation of a constant Q transform,’’ J. Acoust. Soc. Am. (to be published 1992)] will be described. One can then calculate the cross-correlation function of these spectra with the ideal pattern, which consists of ones at the positions of the harmonic frequency components, to obtain the fundamental frequency of the input signal. Extremely accurate values of the fundamental frequency can be obtained using a method based on phase changes of the discrete Fourier transform [J. C. Brown and M. S. Puckette, ‘‘A high resolution fundamental frequency determination based on phase changes of the Fourier transform,’’ submitted to J. Acoust. Soc. Am. (1992)]. Results for a variety of musical instruments will be presented, including recent results on tracking very low frequencies produced by a cello.

A high-resolution fundamental frequency determination based on phase changes of the FFT.

The constant Q transform described recently [J. C. Brown and M. S. Puckette, ‘‘A Real Time Constant Q Transform,’’ submitted to IEEE Trans. Signal Process. (1992)] has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages. For this purpose a frame size of 25 ms or less is required; thus the calculation described previously has been modified so that it is constant resolution rather than constant Q for the lower frequency bins. This calculation as modified serves as the input for a fundamental frequency tracker similar to that described by Brown [J. C. Brown, ‘‘Musical Pitch Tracking using a Pattern Recognition Method,’’ submitted to J. Acoust. Soc. Am. (1992)]. This frequency tracker is designed for musical applications and is based on pattern recognition of the log frequency representation of a sound with harmonic frequency components. Once the fundamental frequency has been chosen by the tracker, an approximation for the phase change in the FFT for a time advance of one sample was used to obtain an extremely precise value for this frequency. Graphical examples are given for musical passages by a violin executing vibrato and glissando. Here the instrumental frequency changes are continuous, and an extremely accurate value is necessary for a precise determination of the fundamental frequency.

General Theory for the Outer Planets

An iterative method for the construction of planetary theories has been developed in order to determine the high order perturbations with respect to the masses. These perturbations are indeed needed to enlarge the validity span of analytical theories up to some million years. The application to the simplified Sun-Jupiter-Saturn problem gives a solution accurate over several ten million years. Throughout the study of the four outer planets we meet with convergence difficulties especially in the determination of fundamental frequencies. One of the results of this study is it shows evidence of long period terms with large amplitude in the mean longitudes: 12 000″ in Saturn longitude, 20 000″ in that of Uranus.

Design Charts and Tables for the Approximate Determination of Fundamental Frequency and Buckling Loads of Circular Plates With Mixed Boundary Conditions

Design Charts and Tables for the Approximate Determination of Fundamental Frequency and Buckling Loads of Circular Plates With Mixed Boundary Conditions

Novel effects in the laser induced fluorescence spectrum of C6F+6

The B̃ 2A2u←X̃ 2E1g(0) laser induced fluorescence excitation spectrum of the hexafluorobenzene cation in a free jet expansion has been measured from 21 500 to 22 580 cm−1. The spectrum displays a number of strong transitions involving the totally symmetric and the Jahn–Teller active vibrations. In addition, many weak transitions involving other vibrational modes are observed using high laser powers. These weak, interspersed transitions are readily detected because the ion is cooled in a supersonic expansion which results in sharp, well resolved lines. These weak transitions derive their intensities by a variety of mechanisms, the most novel of which depends on the presence of mixed cross-quadratic nuclear potential terms in the ground (2E1g) state. It is shown that these terms permit the observation of transitions from the vibrationless level of the ground state to combination levels of the excited state involving two modes of different symmetries. The identification of transitions of this type provides the first experimental demonstration of the occurrence of mixed cross-quadratic nuclear potential terms in spatially degenerate electronic states. The analysis of the spectrum has allowed overall the determination of fundamental frequencies for 16 of the 20 normal modes of C6F+6 in its B̃ 2A2u electronic state.

Effect of a concentrated mass on large amplitude, free flexural vibrations of elastic plates and beams

This paper presents an approximate solution to the title problem for the following situations: (a) supported and clamped rectangular plates, (b) circular plates with edges elastically restrained against rotation, and (c) beams with ends flexibly attached. The approach is quite simple and it is shown that the engineering accuracy achieved is satisfactory from the point of view of the determination of fundamental frequencies in a wide variety of structural elements commonly used in transducer design and aerospace and naval engineering applications.

Clinical estimation of fundamental frequency: the 3M Plastiform Magnetic Tape Viewer

The purpose of this study was to determine the accuracy and reliability of the 3M Viewer in measuring fundamental vocal frequency and to suggest a method of incorporating the 3M Viewer into the clinical measurement of pitch. A total of forty normal speaking persons served as subjects. Recorded sustained terminal vowel segments were obtained from each subject following procedures outlined by Fairbanks and Wilson. The terminal vowel segments were then analyzed utilizing two electronic systems for extracting fundamental frequency (electronic band‐pass filters and digital frequency counter; Kay Elemetrics Sonograph), and 3M Viewer. Measurements made with the 3M Viewer by three observers were submitted to a linear regression analysis. The fundamental vocal frequency estimates from each of the three methods of fundamental frequency determination were submitted to an analysis of variance. Results suggest that the three estimates with the 3M Viewer are not significantly different from one another and that the 3M Viewer method of estimating fundamental vocal frequency is at least as accurate as the other two methods employed in this study.

Vibrations of a circular plate elastically restrained along the edge and carrying a concentrated mass

This investigation deals with the determination of fundamental frequencies of vibration of a circular plate carrying a concentrated mass at the center. The plate is elaatically restrained along the edge and subjected to a hydrostatic state of in-plane stress. The calculated fundamental frequencies are in excellent agreement with those available in the open literature (rigid clamp along the edge and no in-plane forces). The method of solution consists of expanding the displacement function in a simple polynomial which identically satisfies the boundary conditions. A variational method is then used to gencrate the frequency equation. The approximate solution is also valid when the mass is placed off-center.