Fundamental frequency

About: Fundamental frequency is a research topic. Over the lifetime, 8941 publications have been published within this topic receiving 131583 citations.

Multiple Fundamental Frequency Estimation by Summing Harmonic Amplitudes

Abstract: This paper proposes a conceptually simple and computationally efficient fundamental frequency (F0) estimator for polyphonic music signals. The studied class of estimators calculate the salience, or strength, of a F0 candidate as a weighted sum of the amplitudes of its harmonic partials. A mapping from the Fourier spectrum to a “F0 salience spectrum” is found by optimization using generated training material. Based on the resulting function, three different estimators are proposed: a “direct” method, an iterative estimation and cancellation method, and a method that estimates multiple F0s jointly. The latter two performed as well as a considerably more complex reference method. The number of concurrent sounds is estimated along with their F0s.

Fixed point analysis of frequency to instantaneous frequency mapping for accurate estimation of F0 and periodicity

Abstract: An accurate fundamental frequency (F0) estimation method for non-stationary, speech-like sounds is proposed based on the differential properties of the instantaneous frequencies of two sets of filter outputs. A specific type of fixed points of mapping from the filter center frequency to the output instantaneous frequency provides frequencies of the constituent sinusoidal components of the input signal. When the filter is made from an isometric Gabor function convoluted with a cardinal B-spline basis function, the differential properties at the fixed points provide practical estimates of the carrier-to-noise ratio of the corresponding components. These estimates are used to select the fundamental component and to integrate the F0 information distributed among the other harmonic components.

A heterogeneous nonlinear attenuating full- wave model of ultrasound

Abstract: A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A -78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.

Detection of terahertz radiation in gated two-dimensional structures governed by dc current

Abstract: We present theoretical and experimental studies of the direct current effect on the detection of subterahertz and terahertz radiation in gated two-dimensional structures. We developed a theory of the current-driven detection both for resonant case, when the fundamental frequency of plasma oscillation is large compared to inverse scattering time, ${\ensuremath{\omega}}_{0}\ensuremath{\tau}⪢1$, and for the nonresonant case, ${\ensuremath{\omega}}_{0}\ensuremath{\tau}⪡1$, when the plasma oscillations are damped. We predict that, in the nonresonant case, even a very small dc current would increase the detection amplitude up to two orders of magnitude. Physically, this increase is related to an abrupt transition from the linear to saturation region near the knee of the current-voltage characteristic. When the current increases up to the saturation value, the electron concentration near the drain becomes very low and can be strongly affected by a small external field. As a consequence, the two-dimensional channel becomes extremely sensitive to external perturbations. In the resonant case, the detection amplitude has maxima when the radiation frequency is equal to fundamental plasma frequency and its harmonics. We predict that the effective linewidths of the respective resonances would decrease with the increasing current. Physically, this happens because dc current shifts the system towards the plasma wave instability. At some critical current value, the width corresponding to the fundamental frequency would turn to zero, indicating the onset of plasma waves generation. Our experimental measurements performed on $\mathrm{GaAs}$ HEMT confirm the theoretical predictions.

Dynamic Phasor and Frequency Estimates Through Maximally Flat Differentiators

Abstract: Estimates of the dynamic phasor and its derivatives are obtained through the weighted least squares solution of a Taylor approximation using classical windows as weighting factors. This solution leads to differentiators with ideal frequency response around the fundamental frequency and to very low sidelobe level over the stopband, which implies low noise sensitivity. The differentiators are maximally flat in the interval centered at the fundamental frequency and have a linear phase response. Therefore, their estimates are free of amplitude and phase distortion and are obtained at once. No further patch is needed to improve their accuracy. Examples of dynamic phasor estimates are illustrated under transient conditions. Special emphasis is put on frequency measurements.