Methods for propagating a non sinusoidal signal without distortion in dispersive lossy media

Systems and methods are described for transmitting a waveform having a controllable attenuation and propagation velocity. An exemplary method comprises: generating an exponential waveform, the exponential waveform (a) being characterized by the equation Vin=De−A[x−vt], where D is a magnitude, Vin is a voltage, t is time, ASD is an attenuation coefficient, and vSD is a propagation velocity; and (b) being truncated at a maximum value. An exemplary apparatus comprises: an exponential waveform generator; an input recorder coupled to an output of the exponential waveform generator; a transmission line under test coupled to the output of the exponential waveform generator; an output recorder coupled to the transmission line under test; an additional transmission line coupled to the transmission line under test; and a termination impedance coupled to the additional transmission line and to a ground.Board of Regents, University of Texas Syste

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed

Time synchronization and controlled asynchronization of remote trigger signals

A mechanism is disclosed for transmitting pulses onto respective cables so that the pulses arrive at the remote ends of the respective cables in synchronized (or controllably asynchronized) fashion. First, the round-trip time of flight of each cable is measured using speedy delivery pulses, i.e., pulses whose leading edges have exponential shape. Second, a calculation is performed to determine the input delay(s) between the pulses that would produce desired output delay(s). For example, it may be desirable that the pulses arrive at the respective remote ends at the same time, in which case the desired output delay(s) is (are) zero. Third, the same speedy delivery pulses are transmitted onto the respective cables so that the interpulse delay(s) conform to the computed input delay(s). Thus, the desired output delay(s) are achieved at the remote ends of the cables.Board of Regents, University of Texas Syste

A Model Quantifying Pulse Propagation Through Layered Attenuative Media

The influence of attenuation on pulsed ultrasonic signals has been under intense investigation especially in biomedical applications where it is most noticeable. Because attenuation depends on frequency, signals will be dissipated and dispersed as they travel through the medium. For many materials attenuation can be measured in vivo using a transmit and receive system where a pressure signal goes through a layered medium of fixed dimensions. The amount of attenuation, loosely defined as signal loss, is often found to be linearly or nearly linearly dependent on frequency. From this fact and the notion of causality it is possible to predict the phase angle of the spectrum as a function of frequency. Because this phase is nonlinearly dependent on frequency, the signal will be dispersed. This implies that transient responses experience distortion and the measured velocity of the pulse will be shifted with respect to the sound velocity expected from a lossless medium. In his paper on power law attenuation [1], Szabo has proven the amount of dispersion is maximum when the attenuation is linearly dependent on frequency and correspondingly minimum with a frequency square dependency

Finite difference methods for transient signal propagation in stratified dispersive media

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods

Multipath detection and mitigation of random noise signals propagated through naturally lossy dispersive media for radar applications

This paper describes a methodological analysis of the Brillouin precursor formation to understand the impairments undergone by like-noise and random noise waveforms propagating through naturally dispersive media commonly found in radar applications. By means of a frequency-domain methodology based on considering the frequency response of the medium under study, the effect of these dispersive media on the evolution of an input signal can be seen as frequency filtering. The simulations were performed at a center frequency of 1.5 GHz and for a signal bandwidth of 3 GHz. Four random noise signals were considered: Barker codes, PRBS codes, Frank codes, Costas codes and additive white Gaussian noise. The experienced impairments were assessed in terms of cross-correlation function (CCF) degradation. The differences in the behavior of each type of phase and frequency coded signal to face the dispersive propagation have been demonstrated in terms of parameters used for information retrieval: peak amplitude decay, CCF secondary sidelobe level and multipath detectability. Finally, a frequency filtering approach is proposed to mitigate the impairments due to dispersive propagation under multipath conditions.Xunta de Galicia | Ref. ED431C 2019/26Xunta de Galicia | Ref. ED431G 2019/08Centro Singular de Investigación de GaliciaAgencia Estatal de Investigación | Ref. PID2020-112545RB-C5