Harmonic

About: Harmonic is a research topic. Over the lifetime, 44833 publications have been published within this topic receiving 495922 citations. The topic is also known as: overtone & partial.

Sources of image degradation in fundamental and harmonic ultrasound imaging using nonlinear, full-wave simulations

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). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. 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 beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging.

Harmonic and Musical Wavelets

Abstract: The concept of a harmonic wavelet is generalized to describe a family of mixed wavelets with the structure w m, n (x) = {exp (i n 2π x ) – exp (i m 2π x )}/i( n – m ) 2π x . It is shown that this family provides a complete set of orthogonal basis functions for signal analysis. By choosing the (real) numbers m and n (not necessarily integers) appropriately, wavelets whose frequency content ascends according to the musical scale can be generated. These musical wavelets provide greater frequency discrimination than is possible with harmonic wavelets whose frequency interval is always an octave. An example of the wavelet analysis of music illustrates possible applications.

General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach-Zehnder electrooptical modulator

Abstract: A general derivation of the optical modulation process in a dual-drive Mach-Zehnder modulator (DD-MZM) is introduced. The expressions include all harmonics and are entirely general in terms of bias point. Chromatic dispersion is also included allowing the prediction of a number of important phenomena in photonic signal transmission. Examples of special cases of these general equations are then presented. Similar expressions are introduced for harmonic optical up-conversion through a photonic mixer based on a DD-MZM covering any bias point or phase shift between DD-MZM drives.

Quantum Simulation of High-Order Harmonic Spectra of the Hydrogen Atom

Abstract: Three alternative forms of harmonic spectra, based on the dipole moment, dipole velocity, and dipole acceleration, are compared by a numerical solution of the Schrodinger equation for a hydrogen atom interact- ing with a linearly polarized laser pulse, whose electric field is given by Et = E0ftcos0t + with Gaussian carrier envelope ft = expt 2 / 2 . The carrier frequency 0 is fixed to correspond to a wavelength of 800 nm. Spectra for a selection of pulses, for which the intensity I0 = c0E 0 , duration T, and carrier-envelope phase are systematically varied, show that, depending on , all three forms are in good agreement for "weak" pulses with I0 Ib, the over-barrier ionization threshold, but that marked differences among the three appear as the pulse becomes shorter and stronger I0 Ib. Except for scalings by powers of the harmonic frequency, the three forms differ from one another only by "limit contributions" proportional to the expectation values of the dipole moment ztf or dipole velocity ztf at the end tf of the pulse. For long, weak pulses the limit contributions are negligible, whereas for short, strong ones they are not. In the short, strong limit, where ztf 0 and therefore zt may increase without bound i.e., the atom may ionize, depending on ,a n "infinite-time" spectrum based on the acceleration form provides a convenient computational pathway to the corresponding infinite-time dipole-velocity spectrum, which is related directly to the experimentally measured "harmonic photon number spectrum" HPNS. For short, intense pulses the HPNS is quite sensitive to and exhibits not only the usual odd harmonics but also even ones. The analysis also reveals that most of the harmonic photons are emitted during the passage of the pulse. Because of the divergence of zt the dipole- moment form does not provide a numerically reliable route to the harmonic spectrum for very short few- cycle, very intense laser pulses.

The Harmonic Domain. A frame of reference for power system harmonic analysis

Abstract: The Harmonic Domain is a general frame of reference for power system analysis in the steady state which models the coupling between phases and between harmonics. In this frame of reference the nonlinear components, converted into harmonic Norton equivalents, are combined with the rest of the system and solved iteratively by the Newton-Raphson technique. This paper describes the structure of the new domain and illustrates its potential applications in a small power system with multiple nonlinearities. >