Showing papers on "Fundamental frequency published in 1968"
TL;DR: Several methods of fundamental frequency and period measurement, based on these concepts, are described and the results of computer simulations and analog instrumentations indicate that these new methods compare favorably with, and in some cases exceed, the capabilities of cepstrum analysis.
Abstract: The fundamental frequency of a periodic signal whose fundamental component is not available for measurement can be determined by measuring the frequencies of its higher harmonic components and computing the largest common divider of these frequencies. Similarly, the fundamental period can be determined by measuring the periods of individual harmonics and finding their smallest common multiple. Several methods of fundamental frequency and period measurement, based on these concepts, are described in this paper. The results of computer simulations and analog instrumentations indicate that these new methods. at a considerable reduction in complexity, compare favorably with, and in some cases exceed, the capabilities of cepstrum analysis.
312 citations
TL;DR: In this paper, a third-order theory has been developed to study capillary instability of a liquid jet, and it has been shown that the asymmetrical development of an initially sinusoidal wave is a nonlinear effect with generation of higher harmonics as well as feedback into the fundamental.
Abstract: A third-order theory has been developed to study capillary instability of a liquid jet. The result shows that the asymmetrical development of an initially sinusoidal wave is a non-linear effect with generation of higher harmonics as well as feedback into the fundamental. The growth of the surface wave is found to depend explicitly on the dimensionless initial amplitude of the disturbance and the dimensionless wave-number k of the wave. For the same initial disturbance, the wave is found to have a maximum growth rate at k = 0·7 in agreement with the linearized theory. For the same wave-number, the growth is proportional to the initial amplitude of the disturbance. The cut-off wave-number and the fundamental frequency (or growth rate for the unstable case) of the wave for a given k are found to be different from the linearized theory. Furthermore, at the cut-off wave-number, the present theory shows the disturbance experiences a growth which is proportional to t2. The excellent agreement between Donnelly & Glaberson's experiment and Rayleigh's linearized theory is found to be due to their method of measurement.
265 citations
TL;DR: The vibration greatness of three kinds of pulses such as pulsed sinusoidal, damped and built-up vibrations is obtained in comparison with a continuous sinusoid vibration.
Abstract: Perceptional and emotional responses on continuous sinusoidal vibrations characteriz-ed as vibration greatness and unpleasant or unbearable feeling were reported in the pre-vious papers.In this paper, the vibration greatness of three kinds of pulses such as pulsed sinusoidal, damped and built-up vibrations is obtained in comparison with a continuous sinusoidal vibration. The frequency of the continuous sinusoidal vibration is selected to be the same as the fundamental frequency of each pulse. Ten male subjects sitting erect are given the whole body vibration in vertical and horizontal directions and the hand vibration in vertical direction.Durations and fundamental frequencies of the pulsed sinusoidal vibrations are changed between 0.005 and 6 sec, and 2-300 Hz respectively, but their level is maintained constant. The vibration greatness of the pulsed sine waves increases with their dura-tion up to approximately 2 sec in the frequecy range between 2 and 60 Hz. The rate of the increase can be approximated by the straight line with the slope of 7 dB / decade of duration.The vibration greatness of the damped vibration can be evaluated by peak-to-peak amplitude and duration of initial one period of its fundamental frequency.The vibration greatness of the built-up vibration can be estimated by its maximum peak-to-peak amplitude, fundamental frequency and duration corresponding to the am-plitude 1.5 dB below the maximum peak-to-peak amplitude.The perceptional threshold for the pulsed sinusoidal waves is also measured and can be approximated by the line with the same slope as that of the vibration greatness (7 dB / decade of duration).
131 citations
TL;DR: The judgments both of vowel quality and of musical timbre indicated that small changes in the frequencies of the two lower formants of the sound with the higher fundamental could be reduced to a minimum.
Abstract: Observers gave magnitude estimations of the difference in sound quality between the members of pairs of vowellike synthesized sounds. The observers in one set of experiments were asked to judge differences in vowel quality; those in an analogous set of experiments, differences in musical timbre. The first sound in each pair—the standard—was an imitation of one of six English vowels. The second sound in each pair—the test sound—was derived from the first by modifications of the fundamental frequency, the formant frequencies, or certain combinations of both. When the fundamental of the second sound was raised an octave above the frequency of the first, the estimates of difference—both in vowel quality and in musical timbre—could be reduced to a minimum, if the frequencies of the two lower formants of the sound with the higher fundamental were multiplied by a factor of 1.10. The judgments both of vowel quality and of musical timbre indicated that small changes in the frequencies of the two lower formants mad...
104 citations
TL;DR: In this paper, the exact solution and some approximate solutions for the free vibrations of uniform rectangular curved panels with simply supported edges are given Exact solutions are not available for all boundary conditions and a general energy method, in which the mid surface displacements are represented by truncated double-power series in the mid-surface co-ordinates of the panel, is outlined.
59 citations
TL;DR: In this article, the authors present a method for the maximization of the lowest natural frequency of a structural system of a given weight by varying the stiffness of its component elements, which is based on the Newton-Ralphson method.
Abstract: I integrated structural and mechanical systems, the design criteria may be governed by the fundamental frequency of the structure either to provide a certain precision in control or to prevent damage to the system due to resonance between the mechanical and structural systems. Tracking antennas, radio telescopes, and orbiting reflectors are a few examples of the types of structures for which the frequency consideration becomes exceptionally important. . Turner attempted to minimize the mass of a structure with a specific natural frequency. This problem is governed by a system of nonlinear equations and a solution was obtained iteratively by an adaptation of the Newton-Ralphson method. The procedure consists essentially of starting with a given mass distribution, and hence with a given natural frequency, and then obtaining a series of corrections to the mass distribution until minimum mass is achieved. In many physical problems, the original frequency may not be satisfactory and, hence, the problem of maximization of frequency for a given total mass of the structure becomes important/The objective of this paper is to present a method for the maximization of the lowest natural frequency of a structural system of a given weight by varying the stiffness of its component elements. This problem has been investigated by Taylor for the special case of a bar.
56 citations
TL;DR: Experimental tests have been made on a computer-simulated channel vocoder to see whether pitch perturbation can be effectively simulated by partially replacing voiced excitation by random noise, in appropriate frequency-time portions and shows that partial devoicing of the high-frequency ranges definitely improves speech quality.
Abstract: Aperiodicity in voiced segments of speech may be ascribed to different causes. The magnitude of pitch perturbation is different in different spectral ranges of the signal. To see whether pitch perturbation can be effectively simulated by partially replacing voiced excitation by random noise, in appropriate frequency-time portions, experimental tests have been made on a computer-simulated channel vocoder. The buzz-hiss decision was made separately for three different frequency portions of the signal. The cepstrum technique was used for pitch detection, and separate buzz-hiss switching decisions were made at the synthesizer for each frequency portion. The switching thresholds were controlled, and deliberately "devoiced" versions were compared with regular vocoded speech. The fundamental frequency was determined by the lowband cepstrum. The result shows that partial devoicing of the high-frequency ranges definitely improves speech quality. Further, a comparatively large amount of devoicing is perceptually tolerable.
55 citations
TL;DR: In this article, free vibrations of nonuniform cantilever beams with an end support have been investigated, using the equations of Bernoulli-Euler, and two configurations of interest are treated: (a) constant width and linearly variable thickness, and (b) constant thickness and linear variable width.
Abstract: Free vibrations of nonuniform cantilever beams with an end support have been investigated, using the equations of Bernoulli‐Euler. Two configurations of interest are treated: (a) constant width and linearly variable thickness, and (b) constant thickness and linearly variable width. Charts have been plotted for each case from which the fundamental frequency, the second harmonic, and the third harmonic can be easily determined for various taper ratios. The Tables from which these charts were plotted are also included.
53 citations
TL;DR: Second-harmonic generation was observed in an elastic surface wave propagating in the y direction on the x surface of α-quartz by means of interdigital electrode transducers.
Abstract: Second‐harmonic generation was observed in an elastic surface wave propagating in the y direction on the x surface of α‐quartz The waves were generated and detected by means of interdigital electrode transducers The fundamental frequency was 9 MHz The amplitude of the second‐harmonic signal increased linearly with distance along the crystal surface A nearly perfect square‐law dependence of second‐harmonic power on fundamental power was found The ratio of second‐harmonic to fundamental power was −438 dB at a distance of 22 cm and a fundamental input power of 1 W The results are in quantitative agreement with theory
50 citations
TL;DR: In this paper, a one-dimensional structure with segmentwise constant specific stiffness is considered and a sufficient condition for optimality is established and its use is illustrated by an example, where the number of segments of constant specific stiffness is given, but their boundaries and specific stiffnesses are to be determined to minimize the structural weight.
42 citations
TL;DR: In this article, the fundamental frequency of a Bernoulli-Euler beam with variable cross-section is optimized with respect to its fundamental frequency for a set of homogeneous boundary conditions.
TL;DR: In this article, the authors proposed a high efficiency buncher using the fundamental frequency and its second harmonic to simulate the third one, achieving a gain of 5 with a third harmonic simulated buncher instead of 3 with a classical buncher.
Patent•
20 Sep 1968TL;DR: In this paper, the switching of the switching component to its nonconductive condition is delayed, thereby bridging the shortest or several short noncurrent intervals in a half-cycle of the output voltage when the fundamental frequency or the frequency of the AC output voltage or both are simultaneously increased.
Abstract: A method of operating an inverter having a constant DC input voltage and an AC output voltage having a controlled fundamental frequency during pulse operation with voltage time integrals resulting in an approximately sinusoidal current curve and having a conductance dependent upon the output frequency and also having a switching component comprises delaying the switching of the switching component to its nonconductive condition thereby bridging the shortest or several short noncurrent intervals in a half-cycle of the output voltage when the fundamental frequency or the frequency of the AC output voltage or both are simultaneously increased. The shortest voltage time integral is bridged under the same circumstances. The switching of the switching component to its nonconductive condition is delayed thereby reinserting the noncurrent intervals when the fundamental frequency or the frequency of the AC output voltage or both are simultaneously decreased.
TL;DR: For signals of fundamental frequency greater than approximately 2000 cps, harmonic components have little or no effect on the ability of observers to discriminate differences in frequency, however, below approximately2000 cps differences in the frequency of signals containing harmonically related components are more readily discriminated than differences inThe frequency of sinusoidal signals.
Abstract: The effect of the presence of harmonics on frequency discrimination is measured as a function of the frequency of the fundamental component of the signal. For signals of fundamental frequency greater than approximately 2000 cps, harmonic components have little or no effect on the ability of observers to discriminate differences in frequency. Below approximately 2000 cps, however, differences in the frequency of signals containing harmonically related components are more readily discriminated than differences in the frequency of sinusoidal signals. These findings relate to the dependence of frequency discriminability on frequency.
TL;DR: In this article, the fundamental frequency of vibration of simply supported rhombic plates was determined by a simple-branching algorithm, and the results were tabulated and compared with values already available in the literature.
Abstract: The present study deals with the determination of the fundamental frequency of vibration of simply supported rhombic plates. The results are tabulated and compared with values already available in the literature.
TL;DR: In this article, the buckling load and the fundamental frequency of a beam are each computed as a function of the torsional stiffness, which leads to a one-to-one nondimensional relationship between the bucking load and its natural frequency.
Abstract: There are analytical methods for predicting the buckling loads of columns with the boundaries ideally fixed, i.e., simply supported or built-in, or partially fixed. Vibration-test results may furnish a practical method of measuring the fixity. In this investigation a beam, that may or may not be loaded as a column, is assumed to have a torsional spring at each end such that a zero torsional stiffness corresponds to a simply supported end and an infinite torsional stiffness corresponds to a built-in end. From a Rayleigh-Ritz analysis, the buckling load and the fundamental frequency of the beam are each computed as a function of the torsional stiffness. This procedure leads to a one-to-one nondimensional relationship between the buckling load and the natural frequency. From these calculations, it is seen that regardless of the degree of clamping of one end relative to the other end, all that is needed to predict the buckling load within a 15-percent range is a knowledge of the theoretical buckling load of the simply supported column; the theoretical fundamental frequency of the simply supported beam; and the experimental fundamental frequency. Experimental results are presented to support the theory.
TL;DR: In this article, an aperiodic solution for the optimum flat gain response in the frequency domain is obtained by using a computer, solution, which solves the infinite set of simultaneous constraint equations associated with the infinite number of periodically spaced load transmission zero.
Abstract: The gain bandwidth restrictions are considered for a distributed parameter load consisting of a resistor shunted by an open-circuited stub of delay length \tau . An aperiodic solution for the optimum flat gain response in the frequency domain is obtained by using a computer, solution, which solves the infinite set of simultaneous constraint equations associated with the infinite number of periodically spaced load transmission zeros. It is shown that this solution converges to the largest gain bandwidth product when only the fundamental frequency band is permitted and all higher order periodicities of the frequency response are properly suppressed by progressively shifting the center frequency of the higher order passbands, as their gains are attenuated. Furthermore, a new result for optimum flat gain periodic response is obtained. In this case, the equalizer is a cascade of commensurate lines each of length \tau /2 . This gives twice the gain of the best periodic equalizer employing lines equal to the stub length \tau . Finally, synthesis techniques for realizing the optimum periodic equalizer are discussed.
Patent•
23 May 1968
TL;DR: In this article, the authors describe a system for generating polyphase odd harmonics of a fundamental frequency derived from but one phase of a high power polyphase source, both the magnitude and relative phase of the harmonics with respect to the fundamental being variable and controllable.
Abstract: : The patent describes a system for generating polyphase odd harmonics of a fundamental frequency derived from but one phase of a high power polyphase source, both the magnitude and relative phase of the harmonics with respect to the fundamental being variable and controllable. The harmonic may be injected into a polyphase aircraft power system to both evaluate the response thereto and provide harmonics of equal magnitude but opposite phase relation to balance out inherent aircraft system harmonics.
TL;DR: In this paper, a nonlinear one-dimensional mathematical model, which includes the reactive nonlinearities due to the spatial variation of E, is developed, indicating that under certain electron density and capacitor-plate spacing conditions strong harmonic resonances and an antiresonance are present.
Abstract: Microwave harmonic generation in a plasma capacitor is investigated both theoretically and experimentally. Deficiencies of previous harmonic generation theories are pointed out and a nonlinear one-dimensional mathematical model, which includes the reactive nonlinearities due to the spatial variation of E, is developed. This nonlinear plasma capacitor model indicates that under certain electron-density and capacitor-plate spacing conditions strong harmonic resonances and an antiresonance are present. The antiresonance occurs when n ω = ω p and the resonances occur when n ω ≳ ω p , where ω p =plasma frequency, ω= the fundamental frequency, and n is the harmonic number. Harmonic generation in a number of gases is investigated experimentally in a coaxial discharge structure. Third-harmonic (9-GHz) efficiencies of up to 13 percent, and third-harmonic output power in excess of 600 mW are reported. Double-probe and microwave-scattering measurements show that enhanced harmonic generation occurs at the above resonances and, hence, substantiate the non-linear plasma capacitor theory. In order to explain the harmonic output power variations that occur with pressure variation and gas type, a graphical method of analysis based on experimental fact and pressure-collision frequency-electron energy curves is presented. This method of analysis not only yields results that compare qualitatively with experimental observations, but it may also possibly be used to design and predict the performance of future plasma frequency multipliers.
TL;DR: In this paper, the fundamental frequency of vibration of clamped and simply supported plates stiffened in two perpendicular directions and carrying concentrated masses is calculated using polynomial approximations and variational techniques.
Abstract: The present study deals with the calculation of the fundamental frequency of vibration of clamped and simply supported plates stiffened in two perpendicular directions and carrying concentrated masses. It is assumed that the stiffeners are closely spaced and that their height is moderate when compared with the thickness of the plate. Use of polynomial approximations and a variational technique simplifies the calculations considerably. The approach is also applicable in the case of plates of complicated boundary shape. Numerical calculations are presented for a clamped square plate with ribs in one direction, and the results are in good agreement with those obtained following the “orthotropic‐plate” approach.
TL;DR: In this article, the frequency equation for a uniform simply supported beam is reduced to the same cubic as for a plane, elastically supported lamina, and the modes associated with these frequencies are characterized each by a nodal axis (or virtual hinge) which is parallel to the axis of the undeformed beam.
TL;DR: In this paper, a simple method was developed for computer experiments on the disc model of the confined electron beam, and the a.c. beam current components of the lowest harmonics (lω, 2ω, 3ω) in the two-resonator klystron were studied.
Abstract: A simple method is developed for computer experiments on the disc model of the confined electron beam. The a.c. beam current components of the lowest harmonics (lω, 2ω, 3ω) in the two-resonator klystron are studied. A number of hollow and solid beam geometries are investigated. The maximum obtainable relative a.c. current amplitudes are in general larger: (a) in thin beams than in wide beams, (b) in beams inside a conducting tube than in beams without tube, (c) in solid beams than in hollow beams. The largest fundamental frequency current amplitude obtained is about l.25i0.
Patent•
17 Jun 1968
TL;DR: In this article, the analog signals at harmonically related frequencies were provided by appropriately filtering a rectangular wave signal produced by a digital to analog converter, which was then used to obtain a coarse error signal.
Abstract: A multiple-speed position-measuring system comprising a plurality of position-measuring devices of different significances, the relatively movable members of the devices being connected together for movement at the same mechanical speed. The improvement resides in supplying analog signals, at a certain frequency, to one of the devices, and supplying to other of the devices analog signals at frequencies harmonically related to the certain frequency, the devices thereby having sensitivities in proportion to the respective frequencies. For example, a device supplied with a fundamental frequency F may provide a coarse error signal, and another device supplied with the 25th harmonic (25F) may provide a fine error signal. Analog signals at harmonically related frequencies may be provided by appropriately filtering a rectangular wave signal produced by a digital to analog converter.
TL;DR: In this paper, an analysis of frequency multiplication with the ideal step-recovery diode in the series-mode of operation is given, where only one conduction angle per period of the fundamental frequency is allowed.
Abstract: An analysis is given of frequency multiplication with the ideal step-recovery diode in the series-mode of operation. Only one conduction angle per period of the fundamental frequency is allowed. The series resistance of the diode is assumed to be different from zero. General and explicit formulae are given for the input impedance, the output power and the power efficiency. The validity of the approximations is discussed throughout. It is shown that the efficiency, -q, of the power conversion is proportional to 1/n2, and that the maximum value for 17 is about 15% for a times 10 multiplier in this series-mode of operation.
TL;DR: In this article, the subharmonic stability of an undamped non-linear two-degree-of-freedom system is investigated theoretically and experimentally, and it is shown that there exist unstable regions inside which the mode initially at rest becomes parametrically excited and oscillates with a fundamental frequency of 1 3, 2 3, or ω depending on the order of instability.
01 Mar 1968
TL;DR: In this article, a simple model for the statistics of the conduction electrons and their interaction with the surface, the Boltzmann equation is solved self-consistently for the fields in the metal, yielding the usual Fresnel solutions plus correction terms which, at optical frequencies and above liquid helium temperatures, are shown to be of the order of one percent.
Abstract: : The memorandum presents a calculation of the classical interaction between laser light and a metal. Using a simple model for the statistics of the conduction electrons and their interaction with the surface, Maxwell's equations and the Boltzmann equation are solved self-consistently for the fields in the metal, yielding the usual Fresnel solutions plus correction terms which, at optical frequencies and above liquid helium temperatures, are shown to be of the order of one percent. When laser light of sufficient intensity is used, a nonlinear polarization is induced and waves of twice the fundamental frequency are produced. For the indicated model and for normal incidence, the second harmonic waves in the metal are calculated and the magnitude of the relative heating is computed. The method for solving the general problem for an arbitrary incidence angle is outlined and the ratio of the average energy flux reflected in the second harmonic to the incident flux is estimated. The relevance to a high-intensity laser experiment is considered and an error in the computation of the reflection coefficient as obtained by Jha is discussed.
01 Jul 1968
TL;DR: In this article, the authors present a general method for solving the problem of steady-state vibrations of an elastic plane structure set in an infinite rigid wall and surrounded by a fluid medium.
Abstract: : The report presents a general method for solving the problem of steady-state vibrations of an elastic plane structure set in an infinite rigid wall and surrounded by a fluid medium. The method is based on a normal mode procedure and the integral transform technique. The displacement function for the structure is assumed in the form of a normal mode series and the modal amplitudes may be evaluated from a truncated infinite set of linear algebraic equations. The effect of the fluid on the structure is given in terms of modal acoustic impedance coefficients. These coefficients are presented as double integral formulas which depend only on the mode shape functions and the parameter ka = (omega)a/c. The radiated acoustic pressure at any point in the fluid is given in a general formula containing the modal amplitudes and certain double integrals that must be evaluated numerically. The general method has been applied to a circular membrane subjected to uniformly distributed dynamic load. The surrounding medium is air on both sides of the membrane in one case and water on one side and air on the other in another case. The calculations have been carried out for a series of frequencies up to and beyond the fundamental frequency for the membrane. (Author)
TL;DR: In this article, a sample of 21 normally hearing adults attempted to match their vocal fundamental frequency to the frequency of tonal signals presented either before or during vocalization under a variety of conditions.
Abstract: Each of a sample of 21 normally hearing adults attempted to match his vocal fundamental frequency to the frequency of tonal signals presented either before or during vocalization under a variety of conditions. He was never informed of his accuracy. The vocalizations were sustained for about 2 sec and were processed through a specially designed “pitch meter”and strip recorder with continuous output and fast rise time. In general, during the first 12‐sec of vocalization, the fundamental frequency shifted either up or down toward the target frequency. Subjects were within about 1% of the target frequency on approximately half the trials, although they showed a tendency to be “on target” for as many as 80% of the trials if they had been “on target” in the preceding trial. None of several measures of vocal pitch matching was related to the more classical auditory pitch matching.] This research was supported in full by a U. S. Public Health Service, Department of Health, Education, and Welfare research grant fr...
TL;DR: In this paper, the fundamental frequency of vibration of simply supported and clamped rib-stiffened plates of elliptical boundary was determined using variational techniques, assuming that the stiffeners are closely spaced and their height is moderate when compared with the thickness of the plate.
Abstract: This investigation deals with the determination of the fundamental frequency of vibration of simply supported and clamped rib‐stiffened plates of elliptical boundary. It is assumed that the stiffeners are closely spaced and their height is moderate when compared with the thickness of the plate. Variational techniques are used to determine the fundamental frequencies. The values compare reasonably well with other results available in the literature. This same straightforward approach can be used for other boundary shapes; experimental determination of the coefficients of the orthotropic biharmonic operator is not required.