Plot Wave Propagation In Matlab

I'm not sure if I even need to include the time t since I only need a snap shot at one instance in time. E5 Matlab 3. 332 views (last 30 days) John on 23 Nov 2011. The task of this question is to write a MATLAB program that will enable the user to calculate wave propagation parameters and find the corresponding E and H fields in the specified medium. this is the script. 2 Jiangsu Marine Resources Development Research Institute, 222005, Lianyungang, China. Follow 81 views (last 30 days) rance low on 2 Nov 2016. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. along the z-axis. Plot and Animate Solutions. sa vladimir. web; books; video; audio; software; images; Toggle navigation. Matlab or any other simulation softwares process everything in digital i. Studying antennas and wave propagation phenomena using interactive graphics and animations becomes nowadays a fundamental tool for describing and understanding electromagnetic concepts. RF propagation describes the behavior of electromagnetic radiation from a point of transmission as it travels through the surrounding environment. In his spare time, Mehmet uses MATLAB Home™ to create educational animations, which he posts for free online, continuing a project that he started during his visiting professorship at the American University of Sharjah. Learn more about em wave propagation 3-d. A two-ray propagation channel is the simplest type of multipath channel. The implementation is to be done in steps given below. Song Yongxian. The package has a sequence of 6 models that have both a transient pulse excitation as well as a sine wave excitation. 1,2 Zhang xianjin1 1. Discover what MATLAB. Hata Okumura model for outdoor propagation; Log distance path loss model. and explains what m, n, and p are. Plot the noisy signal in the time domain. The ElasticMatrix Toolbox uses the partial-wave method [1,3,4] to model elastic wave propagation in multi-layered anisotropic media up to transverse-isotropic symmetry when the wave propagation is along a plane of symmetry. The amplitude and phase spectrums are also plotted. I found this piece of code which effectively draw a 2D wave placing a droplet in the middle of the graph (I almost fully commented it to simplify things) and then letting it expanding till the border, then bouncing back (how can this code do that?. Single-file vectorized implementation of acoustic wave propagation in MATLAB. The factor for each component of the wave can be expressed by:. TRANSMISSION LINE ENDING IN A MATCHING IMPEDANCE. CODING FOR THE FINITE-DIFFERENCE COMPUTATION. ECE 391: Suggested Homework Problems Basic Relationships 1. What if we want a wave to continue on forever? Obviously we cannot deal with an infinitely long wave; however, we can have a boundary condition that will. SPONSORING I MONiTORING AGENCY NAME(S) AND ADDRESS(ES) 10. In addition to the experimental study, a numerical study was also conducted. The tool has a unique feature over exis ting one-way parabolic equation (PE)-based codes, because it. Please try using the fft and fftshift functions to compute the Fourier spectrum, and then plot the magnitude response (using the abs function) versus frequency (in hertz). Book Description. In this paper, the effect of the obstacle in an environment such as building on the electromagnetic wave propagation has been analyzed by MATLAB simulation software for TMz mode. Please copy and the paste the following code in matlab editor or matlab command window. To solve problems in electromagnetism, you simply discretise in both space and time the Maxwell’s curl equations with a central difference approximation. for elastic wave propagation from a point source. stem (Y) plots the data sequence, Y, as stems that extend from a baseline along the x -axis. You can use a two-ray channel to simulate propagation of signals in a homogeneous, isotropic medium with a single reflecting boundary. Wave Propagation in a Multi-Layered Composite; Elastic Wave Scattering w/ Embedded Sphere Using k-Wave/Matlab; Longitudinal Wave Propagation Using k-Wave and Matlab; Wave Propagation. You should implement that condition in your code. Discover what MATLAB. I want to plot these in a 3-dimensional space. •Gain intuitive understanding of optics and propagation •Coherent and incoherent imaging systems Tools: •Complex MATLAB Coding Principles of Wave Optics •Understand plane wave propagation •Understand interference •Understand basic concepts of wave diffraction Pre-requisites •ECE 311with a C or higher; ECE342 with a C or higher IN OUT. The wave propagation phenomenon was simulated for voided and stratified regions using the. Free essays, homework help, flashcards, research papers, book reports, term papers, history, science, politics. This includes ray optics, Fourier Optics, Gaussian beam propagation, the split-step beam propagation method, holography and complex spatial filtering, ray theory. NFFT=1024; %NFFT-point DFT X=fft (x,NFFT); %compute DFT. (Finite or Boundary Element Methods or MATLAB Solutions) 2. In this example, we will draw. , Columbia, SC, USA 29208. 1 Students should check this, to get a better handle on efficiently spotting orthogonality relations when integrating well-chosen eigenfunctions of Hermitian operators. Regardless, you've come here for answers. – dynamic ruptureon non-planar faults and seismic wave radiation (Madariaga et al. Skip to content. [email protected] The values of X for both the graphs will be the same, we will only change the values of Y by changing the equation for each wave. In this section, we model a plane wave impinging on an air-water interface assuming the depth of water is infinite (see. Installation. If Map is a siteviewer object with buildings specified, the terrain elevation is adjusted to include the height of the buildings. Plotting waves in 2d. Recommended for you. A comprehensively revised version of the authors' earlier book Principles of Applied Optics, Contemporary Optical Image Processing with MATLAB brings out the systems aspect of optics. The book is clearly written and abundant of excellent examples in MATLAB giving to the reader a lot of step-by-step introductions as well as understanding of the waves propagation. What if we want a wave to continue on forever? Obviously we cannot deal with an infinitely long wave; however, we can have a boundary condition that will. PROPAGATION OF ELECTROMAGNETIC WAVES IN FREE SPACE. The string tension is FT = 9. The blue arrow shows the direction of propagation of the plane wave. The pulse parameter is A = 0. reliable results for all environments, we’ve employed this method in MATLAB routines to simulate acoustic wave propagation. Read "Radio Wave Propagation and Channel Modeling for Earth-Space Systems" by available from Rakuten Kobo. MATLAB >> 2D FDTD Simulation of wave Propagation. Learn more about sine wave, amplitude, sine, wave, frequency, time, sin, cosine, cos, university, plot, ametuer. for elastic wave propagation from a point source. In order to better study the propagation characteristics of electromagnetic waves within the medium, the simulation of the electromagnetic wave propagation in water and oil were conducted using MATLAB, and variation of the electric field and magnetic field vector with time were obtained. Wave Propagation in Inhomogeneous Materials - BESTOSO 6. plz give some more suggestion. ABSTRACT – A numerical code is introduced for SH seismic wave propagation in heterogeneous linear-viscoelastic media, based on the pseudo-spectral Fourier method. I am interested in plotting dispersion curves based on SAFE method. To add a directory to the MATLAB path, either use the pathtool on the command line, or select "Set Path" from the menus in the main MATLAB window. Line 7: Here we are using the plot function to create a graph for the given x and y values we have generated. Introduction. DOING PHYSICS WITH MATLAB TRAVELLING WAVES ON STRINGS Ian Cooper. The Implementation Is To Be Done In Steps Given Below. Question: The Task Of This Question Is To Write A MATLAB Program That Will Enable The User To Calculate Wave Propagation Parameters And Find The Corresponding E And H Fields In The Specified Medium. Page 10: My MATLAB® implementation of double slit diffraction estimated as the wave propagates through the wave guide. Notaroˇs • 156 figures generated in MATLAB with plots of geometries of structures, vector fields, guided and unbounded waves, wave polarization curves, Smith charts, transient signals, antenna patterns, etc. Wave Propagation Analysis and Modeling of Radio Wave Propagation Wave Propagation and Scattering in Random Media: 001 Residential Inspector's Guide to Codes, Forms, & Complaints (Residential Inspector's Guide to Codes, Forms, and Complaints) Aqueous Dielectrics (Studies in. Codes for Acoustic Propagation. In that downsampling process, aliasing may appear. Analog Domain. Notaroˇs • 156 figures generated in MATLAB with plots of geometries of structures, vector fields, guided and unbounded waves, wave polarization curves, Smith charts, transient signals, antenna patterns, etc. while a numerical simulation (qm_bound, qm_propa) or our movie generator is running. the purposes from this paper are driving and simulating the propagation of a wave by using Finite Difference Time Domain Modeling Analysis (FDTD), by drive the corresponding FDTD codes from Maxwell's equation and simulate these codes in MATLAB. The writing style is very engaging. The string tension is FT = 9. WidebandTwoRayChannel models a wideband two-ray propagation channel. In this project, the filtering process of both GPS Total Electron Content (TEC) and magnetic field from GPS and magnetometer measurements, respectively are automated by using GUI with several. Q3 [MATLAB]. Schmidt, "Numerical Simulation of Optical Wave Propagation With Examples in MATLAB" English | 2010-08-05 | ISBN: 0819483265 | 212 pages | PDF | 2. Unwrapped phase for tilted plane-wave propagation from under. It is seen that in the left case, a waveguiding. Wave Propagation in a Multi-Layered Composite; Elastic Wave Scattering w/ Embedded Sphere Using k-Wave/Matlab; Longitudinal Wave Propagation Using k-Wave and Matlab; Wave Propagation. The package has a sequence of 6 models that have both a transient pulse excitation as well as a sine wave excitation. Plotly Graphing Library for MATLAB ® > Scientific > Stem Plot. Coleman and J. Instead, it connects phenomenological approaches with comprehensive microscopic formulations to provide a new and sufficiently broad physical perspective. Follow 107 views (last 30 days) kavya saxena on 1 Sep 2012. ; Gusachenko, L. m: % % Filename: example8. Wave Propagation in Poroelastic Media 7. Research on guided wave propagation in isotropic flat plates has been quite intensive in the past decade. This course discusses theoretical concepts and analysis of wave problems in science and engineering. The plot assumes the polarization to be horizontal, so the tilt angle is 0. Equations and indicate that the amplitude of an electromagnetic wave propagating through a conductor decays exponentially on a characteristic lengthscale, , that is known as the skin-depth. Q3 [MATLAB]. Matlab and in simulation programs like Ansys or Comsol is beneficial. pm = propagationModel(___,Name,Value) sets properties using one or more name-value pairs. For electromagnetic waves, the wave function represents the electric field or magnetic field; for sound waves, the wave. 100-105: Publication Date: 08/2017: Origin: CROSSREF: DOI: 10. Question: Write A MATLAB Script To Plot The Exponential Fourier Series Expansion Of A Full Rectified Sine Wave For 2, 10, 40 Harmonics. A generalized representation of this wave can be obtained as the partial differential equation. Under Wave Phase Propagation choose Internal Wave. An elliptically polarized wave with an axial ratio of 1. Simulation & computation principles - Matlab code. , emacs or notepad). A small piece of code may be useful to understand the working of plot of electromagnetic wave and ‘movie’ command. A MATLAB-Based Virtual Tool for Simulations of Wave Propagation Inside a Parallel-Plate Waveguide [Testing Ourselves] Authors: Apaydin, Gokhan; Sevgi, Levent: Affiliation: AB(0000-0003-1129-6268) Publication: IEEE Antennas and Propagation Magazine, vol. The phased. Anticipating that many students lack specialized training in magnetism and magnetics, Magnetics, Dielectrics, and Wave Propagation with MATLAB® Codes avoids application-specific descriptions. Regardless, you've come here for answers. If you want a different type of plot, look under Edit:Plot Configurations. Plots and an animation of a plane wave propagating in the +Z direction. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. You can solve PDEs by using the finite element method, and postprocess results to explore and analyze them. It seems like I messed it upp somewhere. plot(t,x) I don't really see how more samples will change things, but you can just change the linspace parameters. For example, if we were to change the material from steel to aluminum, the wave speed would change from 5. Problem : There is no wave propagation velocity c to calculate critical time step size. Constant Q-Wave Propagation and Attenuation EINAR KJARTANSSON Rock Physics Project, Department of Geophysics, Stanford University, Stanford, California 94305 A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. With different placement of the lenses the final beam waist (radius of the narrowest part) is different. 1994-05-01. You should implement that condition in your code. This normalizes the x-axis with respect to the sampling rate. Wave Propagation in Free Space Simulations 1. ISBN 1-58488-262-X 1. wave propagation grape code. DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS. it gives a rectangular inclind plane, not like a wave propagation in surface. Wave Propagation in Anisotropic Medium. As the complexity of the indoor propagation environment so that the accuracy of analyzing the millimeter wave propagation characteristics are affected. 2011-05-03 Traveling Wave Analysis of Partial Differential Equations: Numerical and Analytical Methods with Matlab and Maple - No Links; 2010-07-20 Numerical Simulation of Optical Wave Propagation With Examples in Matlab; 2020-01-22 Introductory MATLAB Lab Manual: Humanitarian Data Analysis and Mathematical Models (with MATLAB Beginner's Guide). Let’s consider the following examples. Language and environment: Matlab Author(s): Matthew M. For example, subplot(3,1,1) would create a layout for 3 plots stacked vertically, and signal the plot command to graph in the top plot. Featured on Meta. In the absence of free charge and current densities the Maxwell equations are. Use features like bookmarks, note taking and highlighting while reading Magnetics, Dielectrics, and Wave Propagation with MATLAB® Codes. Other wave types cannot propagate. Format Member Price Non-Member Price; Softcover: $56. m can be used to compute the re ection response from a multilayer dielectric structure. As far as I can tell it's not part of base MATLAB. Path loss is computed along the shortest path shortest path through space connecting the transmitter and receiver antenna centers. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. The effective dielectric constant is also a function of frequency. By default the signal. In the absence of free charge and current densities the Maxwell equations are. It is also possible to obtain the variation of voltage at the. The VLTI as a “real world” application example is presented. Radar Systems Analysis and Design Using MatLab. Simulations for rigid and free surface boundary conditions were made. With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves. It is used to predict the propagation loss for a wide range of environments, whereas, the Friis free space model is restricted to unobstructed clear path between the transmitter and the receiver. A MATLAB-Based Virtual Tool for Simulations of Wave Propagation Inside a Parallel-Plate Waveguide [Testing Ourselves] Authors: Apaydin, Gokhan; Sevgi, Levent: Affiliation: AB(0000-0003-1129-6268) Publication: IEEE Antennas and Propagation Magazine, vol. Active 9 months ago. Since in-plan and out-of-plan motions are coupled for the transversely isotropic medium with a tilted symmetry axis, 3-D simulation seems necessary in. MATLAB program for square wave generation. Enter the command p = plot (indep, dep1, indep, dep2) in the command window. You can do th. Example 1: Plot data from the NOMADS Data Server. It lists each variables in the current workspace, together with information about its size, density, complexity, etc. and explains what m, n, and p are. %Requirement: For plotting 2 periods of the signal fs = 100000; %100KHz sampling frequency f = 1000; %1KHz signal frequency t = 0:1/fs:2*(1/f);. In order to match the incident and transmitted wave at the boundary, the transmitted wave will change its direction of propagation. Both fields travel at z direction. All Graduate Theses and Dissertations. pm = propagationModel(___,Name,Value) sets properties using one or more name-value pairs. The author has extensively revised chapters on radar cross-section and polarization, matched filter and radar ambiguity function, and radar wave propagation. Numerical Simulation of Optical Wave Propagation With Examples in MATLAB (SPIE Press Monograph Vol. Use this information to remove unwanted peaks by specifying a 'MinPeakDistance'. Plot and Animate Solutions. how to plot a wave propagation using surface plot. The book is clearly written and abundant of excellent examples in MATLAB giving to the reader a lot of step-by-step introductions as well as understanding of the waves propagation. the purposes from this paper are driving and simulating the propagation of a wave by using Finite Difference Time Domain Modeling Analysis (FDTD), by drive the corresponding FDTD codes from Maxwell's equation and simulate these codes in MATLAB. The initial recording of the P wave lasts for approximately 21ms (65 -44) and the amplitude is not greater than 0. The peak of the pulse takes 10 s to move from position x = 0 to x = 30 m, hence the velocity as expected is 3. Single-file vectorized implementation of acoustic wave propagation in MATLAB. Solution to the 2-D Wave Equation using finite difference method (Matlab). MATLAB is now employed in more than two thousand universities and the user community throughout the world numbers in the thousands. The user provides her own Matlab function to calculate the "sum-of-squares" function for the likelihood part, e. The values of X for both the graphs will be the same, we will only change the values of Y by changing the equation for each wave. The 2D FFTs are accomplished using fft2. Very simply they look like and. The book is clearly written and abundant of excellent examples in MATLAB giving to the reader a lot of step-by-step introductions as well as understanding of the waves propagation. Cut and Paste. Given tune. To create a polynomial in Matlab, simply enter each. 6 Ray Optics using MATLAB 37 2. If you want a different type of plot, look under Edit:Plot Configurations. Path loss, returned as a scalar or M-by-N arrays with each element in decibels. 01: MATLAB M-FILE FOR PLOTTING A SINE WAVEFORM. Supported Colormaps MATLAB supports a number of built-in colormaps, illustrated and described below. The effective dielectric constant is also a function of frequency. I am interested in plotting dispersion curves based on SAFE method. Typing plot(z) will plot the values of z against a list of 1,2,3,4,5, etc. NCTOOLBOX: A MATLAB toolbox for working with common data model datasets. How to draw three dimenstional plots in MATLAB? MATLAB 3D plot examples explained with code and syntax for Mesh, Surface Ribbon, Contour and Slice. In: Proceedings of the 16th International Symposium on Nondestructive Testing and Evaluation of Wood, October 12-14, 2009, Beijing, China. Follow 107 views (last 30 days) kavya saxena on 1 Sep 2012. I think you will see that there is some low-frequency noise or interference superimposed on the signal-of-interest. In phase and quadrature components of a sine wave and a cosine wave Hi, I have a question that seems simple but is surrounding my mind. True , Thank You for correcting me in that n is parallel to r. GOV Technical Report: A Variable Grid FDM Technique for Treating Solid-Liquid and Solid-Air Boundaries in Wave Propagation Modeling of Elastic Waves. What am I doing wrong?. Given a sinusoidal wave v(z;t) = 5sin(ˇ=6 + 4ˇz ˇ109t) (V), where zis measured in meters and tis measured in seconds. BeamLab is an award-winning set of simulation tools for beam propagation through optical devices and waveguides in your familiar MATLAB ® environment — no hassle with learning a new proprietary language or CAD tools, and utmost flexibility in post-processing and editing of any output data and graphs. there is no such feeling of wave. The trick then is to make a Polygon out of each half wave. I am interested in plotting dispersion curves based on SAFE method. Simulation & computation principles - Matlab code. For better efficiency, figure object, axes object, and plot objects should be handled manually. Analogous to the discussion about the direction of the 1D solutions, the wave in Eq. The first is to introduce some traditional topics such as matrix formalism of geometrical optics, wave propagation and diffraction, and some fundamental background on fourier optics. Wave Propagation is a natural phenomenon that is important in many physical systems. the low frequency region of the time-frequency plots. The red dot represents the model parameter set that generated the nominal model results in Fig. Active 9 months ago. Includes a GUI for creating a beamline and interactively viewing it in 3D. Plot and Animate Solutions. Learn more about em wave propagation 3-d. The electromagnetic wave is simulated in MATLAB is by using 'movie' command. The environmental effects include these from the Martian. The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. The wave animations illustrate wave characteristics and particle motion as listed in Table 1. Radio Wave Propagation and Parabolic Equation Modeling is a critical resource forelectrical, electronics, communication, and computer engineers working on industrial and military applications that rely on the directed propagation of radio waves. The training is done using the Backpropagation algorithm with options for Resilient Gradient Descent, Momentum Backpropagation, and Learning Rate Decrease. The plot command also happens to be one of the easiest functions to learn how to use. This Demonstration simulates Gaussian beam propagation and transformation by two lenses. Begin your diagram from the lower left of the window. Use of Matlab and/or Maple is uncouraged. This is an important theory in its own right because explorationists often assume that wave propagation in rocks can be approximated by acoustic theory so that they can simplify their data processing algorithms. Polynomials In Matlab, a polynomial is represented by a vector. Computes wave height using Green's Law. This numerical approach complements the analytical approach followed in §1. [email protected] Tsunami Inundation: Another use of the Propagation Data base is the use of linear combinations of the pre-computed events in the Propagation Database as input for forecast inundation models that numerically predict tsunami wave height, current speeds, and inundation extent for a specific coastal area of interest. My problem is that I need to make another plot in which I have a rectangular wave which changes from Vin to -Vin when the threshold is reached by the sine wave. Abstract This handbook examines the effects of the Martian environment on radio wave propagation on Mars and in the space near the planet. Active 7 months ago. Doing Physics with Matlab 2 Introduction We will use the finite difference time domain (FDTD) method to find solutions of the most fundamental partial differential equation that describes wave motion, the one-dimensional scalar wave equation. txt file (8). account for fringing and the wave propagation in the line. For example, the singularities of the global matrix give the dispersion curves, and by specifying an incident wave, the resulting wave-field throughout the structure can be calculated. Audio Processing by MATLAB #1 1. Active 9 months ago. The aim of this study is to investigate the AE wave propagation in a single layer, an un-bonded double-layer and an adhesively-bonded aluminium joint, with both in-plane and out-of-plane sources, to provide more insight into the propagation of AE waves excited by defect propagation in bonded joints. Wave Propagation in a Multi-Layered Composite; Elastic Wave Scattering w/ Embedded Sphere Using k-Wave/Matlab; Longitudinal Wave Propagation Using k-Wave and Matlab; Wave Propagation. Aimed at a single-semester course on antennas at the undergraduate level, Antennas and Wave Propagation provides a lucid explanation of the fundamentals of antennas and propagation. [Jason Daniel Schmidt] -- Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations. Q&A for scientists using computers to solve scientific problems. 59, issue 4, pp. Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations. The output looks pretty much the same as in the other answers, but I generate the wave from a discrete list of points at which the amplitude is calculated. Using MATLAB to visualize Chirkov Standard Map. As the frequency of operation increases, most of the electric field lines concentrate in the substrate. Lots of Blocks. MATLAB Implementation of a Fourier Approach to Optical Wave Propagation 6. Lectures by Walter Lewin. We don't account for derivatives of elastic parameters. Any multi-mixed-path surface wave propagation scenario may be specified by the user together with all the necessary input parameters, and path loss vs. One kind of method of integration is the Monte-Carlo method of integrals named after the famous Monte-Carlo casino for reasons which will be discussed as we solve a problem to find the integral. The wave animations illustrate wave characteristics and particle motion as listed in Table 1. The pink arrow shows polarization of the plane wave. In beam propagation method, a mode is decomposed into different plane waves, which indeed are sinusoids of different frequencies. Solution to the 2-D Wave Equation using finite difference method (Matlab). TRANSMISSION LINE ENDING IN A MATCHING IMPEDANCE. The book presents the latest advances in numerical simulations of optical wave propagations in turbulent media. The guided wave propagation in asymmetrical corrugated plate with different corrugation dimensions are investigated via numerical method. With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves. web; books; video; audio; software; images; Toggle navigation. This example provides a simple demonstration of using k-Wave for the simulation and detection of the pressure field generated by an initial pressure distribution within a three-dimensional heterogeneous propagation medium. MATLAB >> 2D FDTD Simulation of wave Propagation. mmTrace is a deterministic image-based ray-tracing simulation framework for mm-wave propagation developed in MATLAB. BTW, for next time: have a read here and here. Plotting wave equation. The output looks pretty much the same as in the other answers, but I generate the wave from a discrete list of points at which the amplitude is calculated. txt) or read online for free. Consider the string to have a single spatial dimension. plz give some more suggestion. With different placement of the lenses the final beam waist (radius of the narrowest part) is different. Lots of Blocks. y(x, t) = Acos(ωt + βx + ϕ) in this. The writing style is very engaging. Wave Propagation Analysis and Modeling of Radio Wave Propagation Wave Propagation and Scattering in Random Media: 001 Residential Inspector's Guide to Codes, Forms, & Complaints (Residential Inspector's Guide to Codes, Forms, and Complaints) Aqueous Dielectrics (Studies in. Communication Link on Map. m is in your working. It should be about -60 degrees, the same as the second Bode plot. How to plot this signal. The GUI called Washington, (3) RAY, written by Jim Bowlin of Woods Hole. True , Thank You for correcting me in that n is parallel to r. BeamLab is an award-winning set of simulation tools for beam propagation through optical devices and waveguides in your familiar MATLAB ® environment — no hassle with learning a new proprietary language or CAD tools, and utmost flexibility in post-processing and editing of any output data and graphs. Very simply they look like and. MAXWELL’S EQUATIONS and the FDTD Method The theory on which the FDTD is simple. Country unknown/Code not available: N. You must use this format if your Z data does not fall on a. Matlab plots the graph on a figure with a limited number of screen pixels. High Frequency Surface Wave Radars (HFSWR) use vertically polarized electromagnetic (EM) waves in the lowerhalfofthe HFband(3-15MHz) [1,2]. The result, X, is a 3-by-1000 matrix. How to fit a sine wave – An example in Python If the frequency of a signal is known, the amplitude, phase, and bias on the signal can be estimated using least-squares regression. Consider a traveling transverse wave on a string. Membrane mechanics is essential for wave propagation. The plots are color coded to match the color of the light by calling the script colorCode. Dear members I am using an open source code COULWAVE to run the wave propagation in a wave flume around a conical island. With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves. If you are not using a workstation, Matlab might have difficulties in handling the movie. You have to keep in mind that the first bin is 0 Hz. E5 Matlab 3. To better understand the code, be ready with your Matlab to test it as we go. wav file in the time and frequency domain, we can analyze a tuning fork recording. In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space. For better efficiency, figure object, axes object, and plot objects should be handled manually. I would like to create a contour plot on polar axes similar to the plots produced by the POLAR function. Type plot (XSource, YSource) and press Enter. Read "Wave Propagation in Fluids Models and Numerical Techniques" by Vincent Guinot available from Rakuten Kobo. That is, the percentage of the waveform that occurs above zero axes is 50% for a square wave. Q&A for scientists using computers to solve scientific problems. Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. Since the wave obeys the well known 1/r^2 Friis equation, it will diminish in intensity with the inverse square of distance. A MATLAB toolbox for seismic wave propagation. In free space, RF signals propagate at a constant speed of light in all directions. The general form of a Pyramidal horn has the following design. The function breaks the figure into matrix specified by user and selects the corresponding axes for the current plot SYNTAX : subplot (m,n,p) - Divides the figure window into m x n matrix of small axes and selects the p th. For example, the following script creates a subplot that displays the signals from chirp and from train, as shown in Fig. how to plot a wave propagation using surface plot. You can see that the output from MATLAB is one period of the DTFT, but it's not the period normally plotted, which is from to. This leads to: The phase portrait is a plot of a vector field which qualitatively shows how the solutions to these equations will go from a given starting point. sine wave, Vp=2V, f=1. Keywords: geometrical optics, ray tracing, physical optics, wave propagation, beam decomposition, Gaussian. The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. Type fun = @ (p) sum ( (YSource – (p (1)*cos (p (2)*XSource)+p (2)*sin (p (1. Fig(2) supports this observation. CODING FOR THE FINITE-DIFFERENCE COMPUTATION. If you are new to MATLAB, please go through our tutorials. University of Arizona, 2005 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN APPLIED MATHEMATICS from the NAVAL POSTGRADUATE SCHOOL March 2013. 9 Flux of energy in harmonic waves 125 6 Plane waves in simple models with plane. I also suffered this problem so i tried it by myself. The function fftshift is used shift the quadrants of the FFT around to see the lowest. and explains what m, n, and p are. (Finite or Boundary Element Methods or MATLAB Solutions) 2. More detailed descriptions of the partial-wave and global-matrix method can be found in [4,5,19,20,21,22,23,24]. Plotting waves in 2d. Thus, the propagation velocity of the liquid was calculated by using. Draw a Sine Wave in Excel and Paste it in PowerPoint. Plane Wave Propagation in Lossy Media : Plane Wave Propagation in Lossy Media: Plane Wave Propagation in Lossy Media: Ch 8 : MT360. This article presents the WaveFormRevealer—an analytical framework and predictive tool for the simulation of guided Lamb wave propagation and interaction with damage. They will make you ♥ Physics. The beam is a part of a X bracing steel frame. Wave Propagation in Viscoelastic Media 4. As far as I know stepinfo can determine if the signal in one square wave. Question: The Task Of This Question Is To Write A MATLAB Program That Will Enable The User To Calculate Wave Propagation Parameters And Find The Corresponding E And H Fields In The Specified Medium. The software used for plotting was MATLAB. and help please ?. How would I implement this neural network cost function in matlab: Here are what the symbols represent: % m is the number of training examples. Wave Propagation - Free download as PDF File (. Fearless Soul Recommended for you. When the wave enters the new medium, the speed of propagation will change. I only get pieces of them and a lot of points that. Read "Seismic Wave Propagation in Non-Homogeneous Elastic Media by Boundary Elements" by George D. 18 Mustafa MUTLU: Application of Rayleigh Probability Density Function in Electromagnetic Wave Propagation Figure 3. Path loss is computed along the shortest path shortest path through space connecting the transmitter and receiver antenna centers. square wave v1 1 0 pulse (-1 1 0. Create a matrix where each row represents a cosine wave with scaled frequency. Enter the command p = plot (indep, dep1, indep, dep2) in the command window. Example 2: Plot data from a WAVEWATCH III ® GRiB file. The function fftshift is used shift the quadrants of the FFT around to see the lowest. One of the most important functions in MATLAB is the plot function. This is what I am trying to do: I have tried everything I know in MATLAB to make that plot, but I still haven't managed to create it. I have written another matlab code which goes like this for plane wave generation: x=linspace(0,99); y=linspace(0,99);. Country unknown/Code not available: N. Most of the theoretical delineations summarized in this tutorial have been implemented in Madagascar with Matlab,. The book is clearly written and abundant of excellent examples in MATLAB giving to the reader a lot of step-by-step introductions as well as understanding of the waves propagation. Description. In this tutorial, I am decribing the classification of three dimentional [3D] MATLAB plot. Just divide the sample index on the x-axis by the length of the FFT. The dispersion relation can then also be written more compactly as ω=c k. In essence, the delay time of the input and output signals was a tabbed time with liquids for groups of propagation time, which contain the propagation time of the leaky Rayleigh wave, longitudinal wave, and Rayleigh wave. Please copy and the paste the following code in matlab editor or matlab command window. Refraction at plane interface The refraction at an interface is described by the Snell's law: 𝑛sin𝜃= 𝑛′sin𝜃′ The Matlab function for refraction at a plane interface takes as input height y of the ray at the interface, slope 𝑢= tan𝜃, thickness of the lens, index of refraction n, and vector z, which is used to plot the ray in. %The QRS-complex consists of three major components: Q-wave, R-wave, S-wave. Homework #11 - DFT example using MATLAB. Here, a new open-source toolbox called ElasticMatrix is described which solves the problem of acoustic and elastic wave propagation in multi-layered media for isotropic and transverse-isotropic materials where the wave propagation occurs in a material plane of symmetry. wave propagation grape code. Sine wave plot using Matlab. The plot command in MATLAB help to create two-dimensional plots. ECE3065 Class Project: CSI Wave Propagation. On the next line you will write a statement to plot the function. wave propagation o ver variable terrain and through homogeneous and inhomogeneous atmosphere. Fearless Soul Recommended for you. sa vladimir. Friis free space propagation model is used to model the LOS path loss incurred in a free space environment, devoid of any objects that create absorption, diffraction, reflections, or any other characteristic-altering phenomenon to a radiated wave. We provide plane-wave propagation path data from a wideband MIMO radio channel sounding measurement in an urban microcell scenario. MATLAB is now employed in more than two thousand universities and the user community throughout the world numbers in the thousands. Constant Q-Wave Propagation and Attenuation EINAR KJARTANSSON Rock Physics Project, Department of Geophysics, Stanford University, Stanford, California 94305 A linear model for attenuation of waves is presented, with Q, or the portion of energy lost during each cycle or wavelength, exactly independent of frequency. There is of course no point in simply copying this info here when you can read in the documentation (see link). What Is the Function of the Linspace in MATLAB? The "linspace" function in MATLAB creates a vector of values that are linearly spaced between two endpoints. Paper theoretical and experimental studies of lamb wave propagation in attenuative composites 1. The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. The book presents the latest advances in numerical simulations of optical wave propagations in turbulent media. 28 plot([0:dx:L] , current) 29 axis([0 L −1 1]) 30 pause(. Search Search. The plot function can be used to display the data. Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. This example provides a simple demonstration of using k-Wave for the simulation and detection of the pressure field generated by an initial pressure distribution within a three-dimensional heterogeneous propagation medium. Schmidt Numerical Simulation of Optical Wave Propagation With Examples in MATLAB (SPIE Press Monograph Vol. I am working on wave propagation in multilayer structures. Download it once and read it on your Kindle device, PC, phones or tablets. Suggest an edit to this page. The generated square wave has a value of 1 for intervals [n π, (n + 1) π) with even n and a value of -1 for intervals [n π, (n + 1) π) with odd n. First, the free space path loss is computed as a function of propagation distance and frequency. Spatial inhomogeneity of excitable media leads to nontrivial spatiotemporal dynamics. In this paper, ray tracing method is used to analyze the situation of ample area and finite-difference time domain is used to analyze the complex area contains a discontinuity point. Use graphics if it can help the explanation. The beam propagation method essentially decomposes a mode into a superposition of plane waves, each traveling in a different direction. m file in MATLAB Press "Run" button oleg. Viewed 2k times 2 $\begingroup$ I am using the following script to plot a sine wave in Matlab: Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. The pink arrow shows polarization of the plane wave. 1 Teaching of advanced wave propagation phenomena in passive waveguide devices using. This gives a step-by-step introduction to the way the simulation functions within k-Wave work. With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves. In radar, the 2D Fourier Transform is used as a fast way to create a map from a series of coherent radar pulses. Plot pole-zero diagram for a given tran. Application of Acoustic Wave Propagation Analysis Methods for Monitoring a Miscible Mixing Zone in Porous Media. Learn more about waves, contour plot. 3D time-domain simulation of wave propagation on a GPU using C++ CUDA code: Plot volumetric data using intersecting planes: Write MATLAB matrix to a k-Wave. Doing Physics with Matlab 2 Introduction We will use the finite difference time domain (FDTD) method to find solutions of the most fundamental partial differential equation that describes wave motion, the one-dimensional scalar wave equation. I got a X value of 14,14 with this and that's the 3 peak, but i see now that i may need to write my full script here because i cant use max(F) command because i use syms z. Instead, it's the period from 0 to. Text books leave much to be desired regarding visualization of wave propagation since they are not animated. Stress wave propagation on standing trees. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. A quantity known as the propagation constant is denoted by the Greek letter gamma, γ. wave propagation grape code. Choose x-axis as time or samples 3. 1 : At Normal Incidence : Wave Reflection at Normal Incidence: Wave Reflection at Normal Incidence. From that we will generate a square function & carrier signal which is a sine wave and perform ASK. These define the properties of the computational grid, the material properties of the medium, the properties and locations of any thermal. This is a page to download code for calculating acoustic modes used for simulating acoustic propagation over long ranges in deep water. The data (x and y) are in same folder of the workspace. Phase change for plane-wave propagation showing that a plane wave propagating along the z-axis will have π units of phase change as it advances one-half a wave44 Figure 2. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. MATLAB algorithms - Free download as Word Doc (. DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS. there is no such feeling of wave in it. Software, Data and Validation examples for ionospheric and tropospheric radio wave propagation and radio noise Rollup Image You are here Home > ITU-R > Study Groups > SG 3 > Software, Data and Validation examples for ionospheric and tropospheric radio wave propagation and radio noise. E5 Matlab 3. First, the free space path loss is computed as a function of propagation distance and frequency. ) And Frequency As Input From The User And Find Whether. Problem : There is no wave propagation velocity c to calculate critical time step size. It takes advantage of the fact that light in such devices predominantly propagates along a particular direction, e. MATLAB中文论坛《高等光学仿真(MATLAB)版》——光波导、激光(含第2版)板块发表的帖子:电子书籍分享:Numerical Simulation of Optical Wave Propagation。. The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. Currently five external simulations are supported; (1) EIGENRAY written by Brian. This gives the propagation speed of the pulse as v = 3. >> plot(x,y); This will produce a plot of the sine wave from 0 to 2pi. I found this piece of code which effectively draw a 2D wave placing a droplet in the middle of the graph (I almost fully commented it to simplify things) and then letting it expanding till the border, then bouncing back (how can this code do that?. As the complexity of the indoor propagation environment so that the accuracy of analyzing the millimeter wave propagation characteristics are affected. ThetaTx" in [rad]), direction of arrival (DOA: "par. To create this article, 22 people, some anonymous, worked to edit and improve it over time. Propagation of an Arbitrary Wave Front • Assume a wave with an arbitrary amplitude given numerically on a grid • Propagation along the zaxis can be calculated in three domains: • Far field (Fraunhofer diffraction propagation) • Near field (Fresnel diffraction propagation) ⇝Peter’s and Bernhard’s talk. A generalized representation of this wave can be obtained as the partial differential equation. Half wave rectifier Matlab code for a sine wave of 5 cycles, the code can be modified a little bit to get more or lesser no of cycles. A MATLAB GUI For Ocean Acoustic Propagation North using one of several standard propagation codes. Basic Example of 1D FDTD Code in Matlab The following is an example of the basic FDTD code implemented in Matlab. If f is an equation or function of two variables, then [min,max] specifies the range for both variables, that is the ranges along both the abscissa and the ordinate. Suppose you want to draw a specific type of plot, say a scatterplot, the first. It is used to predict the propagation loss for a wide range of environments, whereas, the Friis free space model is restricted to unobstructed clear path between the transmitter and the receiver. , from an oscilloscope). Overall distinguishing features of MATLABR-Based Electromagnetics: • The book provides two interwoven themes: presentation and study of electromagnetics using MATLAB and development and discussion of MATLAB for electromagnetics • Can be used to either complement available electromagnetics text, or as an independent resource. Learn more about sin wave, signal processing. It is also possible to inject a plane wave at an angle. About plots generated by the Matlab version of WavePacket. Use the link function to plot the success of the communication between the two sites on a map. Here is the problem: When monochromatic light passes through a narrow slit it produces on a screen a diffraction pattern consisting of bright and dark fringes. Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations. Understanding the propagation characteristics. Codes for Acoustic Propagation. Wave Propagation in Viscoelastic Media 4. Theycover widesea/ocean areas, andaretherefore highlyattractive for continuous surveillance of oceans, harbors, straights, etc. Regional and site-specific first wave and maximum wave height and arrival time can be plotted quickly. DEMO DASH; On This Page. Since the wave obeys the well known 1/r^2 Friis equation, it will diminish in intensity with the inverse square of distance. You see a plot of the points which is helpful in visualizing how this process might work. [C Vittoria]. reliable results for all environments, we’ve employed this method in MATLAB routines to simulate acoustic wave propagation. 1m 10m 20m) r1 1 0 10k. The phased. The Matlab scripts are used to model and create animations for the propagation of a pulse and the transfer of energy along a stretched string. Plot and Animate Solutions. 8 : Wave Reflection and Transmission : MT360. 1 CREWES Research Report — Volume 22 (2010) 5 The saved file may be loaded into the program again later when needed for output plots, or to continue further wavefield propagation. If you downloaded the package of m-files in Part 11 of this tutorial, this function is available to you, provided the file slpfield. This gives a step-by-step introduction to the way the simulation functions within k-Wave work. The simple way, you can draw the plot or graph in MATLAB by using code. 1 Students should check this, to get a better handle on efficiently spotting orthogonality relations when integrating well-chosen eigenfunctions of Hermitian operators. Radar Systems Analysis and Design Using MATLAB, 3rd Edition by Bassem R. are often needed to test various signal processing techniques. In this paper, the effect of the obstacle in an environment such as building on the electromagnetic wave propagation has been analyzed by MATLAB simulation software for TMz mode. Commented: John BG on 4 Jan 2018 I have a matlab code which generates a PWM waveform (basically a square wave) which I print into a pdf file. In this article, we investigate Lamb wave propagation in a beam under lead zirconate titanate actuation/sensing, in which the lead zirconate titanate effects are included. [Jason Daniel Schmidt] -- Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations. where i need to find the max value and position of plot 1 and 2. square() is not a built-in function unless you have the Signal Processing Toolbox. using simulated sine-wave analysis carried out by a matlab program. there is no such feeling of wave in it. wave propagation grape code. Few types of waves like square wave, sawtooth wave, triangular wave, etc. This book presents the physical principles of wave propagation in fluid mechanics and hydraulics. [CODE] #include. 8 : Wave Reflection and Transmission : MT360. pdf), Text File (. COMSOL is the developer of COMSOL Multiphysics software, an interactive environment for modeling and simulating scientific and engineering problems. The same wave propagation analysis performed on different materials would take different amounts of CPU time, depending on the wave speed of the material. The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. You can automatically generate meshes with triangular and tetrahedral elements. This means that our voltmeter will measure the. docx), PDF File (. 062J, WAVE PROPAGATION Fall, 2000 MIT NotesbyC. Download it once and read it on your Kindle device, PC, phones or tablets. The simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero. Free space path loss is based on [1][source code] Rain attenuation is obtained from [2][source code] Gaseous absorption is based on [3][source code] Cloud attenuation is obtained from [4][source code] For the sake of conciseness, only the results at 76 and 86 GHz are listed below. Friis free space propagation model is used to model the LOS path loss incurred in a free space environment, devoid of any objects that create absorption, diffraction, reflections, or any other characteristic-altering phenomenon to a radiated wave. Therefore I want to plot the data in certain range. The Matlab version of WavePacket comes with sophisticated visualization, typically generated "on the fly", i. The electromagnetic wave is simulated in MATLAB is by using 'movie' command. Here Is The Code I Have So Far:% Truncated Trigonometric Fourier Series For A Square. In this paper, the multi-algebraic solitary wave solutions for the internal wave BO equation including the linear velocity term in matrix form are given by the bilinear form. m, the main program, which takes user parameter values, computes the configuration for each time step, displays an image of the configuration for each time, and returns the SIR percentages. The wave never has a value of 0. Bibliographic record and links to related information available from the Library of Congress catalog Note: Electronic data is machine generated. Firstly, define the value of 'x' or other variables range of the. MATLAB, and variation of the electric field and magnetic field vector with time were obtained. The program use pre-calculated Lamb wave velocity to calculate the displacement field through the plate thickness, and along the wave propagation direction. while (1) choice=menu({'Radiation pattern of half wavelength dipole (select your choice)';'By antennatutorials. 0 is a circularly polarized wave; an elliptically polarized wave with an infinite axial ratio is a linearly polarized wave. Research on guided wave propagation in isotropic flat plates has been quite intensive in the past decade. PROPAGATION OF ELECTROMAGNETIC WAVES IN FREE SPACE. Help with plotting triangular wave. The problem is my source is not correctly propagated as I have a problem with creating correct kx values and so the multiplication results with somewhat wrong. When I said 5 mm I meant the x-y axis: element*dx. m, sine wave, wave generation, to and fro wave generation, cosine wave, ploting, homework. This leads to: The phase portrait is a plot of a vector field which qualitatively shows how the solutions to these equations will go from a given starting point. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. I need to plot a sine wave. The maximum amplitude of the wave is set to 7 on the Y. In this special case of line-of-sight (LOS) propagation there are no obstructions due to the earth’s surface or other obstacles. The basic idea:For a moving wave, you consider a particular part of it, it moves. I'm not sure if I even need to include the time t since I only need a snap shot at one instance in time. The programming becomes somewhat challenging (and the run time can become significant) because as a wave is. 1 The magnetic field of a wave propagating through a certain nonmagnetic material is given by H zˆ30cos 108t 0 5y (mA/m) Find (a) the direction of wave propagation, (b) the phase velocity, (c) the wavelength in the material, (d) the relative permittivity of the material, and (e) the. This course discusses theoretical concepts and analysis of wave problems in science and engineering. stem (Y) plots the data sequence, Y, as stems that extend from a baseline along the x -axis. Theycover widesea/ocean areas, andaretherefore highlyattractive for continuous surveillance of oceans, harbors, straights, etc. Two-dimensional wave propagation: double slit simulation; Finite-difference Time-domain (FDTD) Method for 2D Wave Propagation. In PyOptica it is always checked before propagation; if the requested distance violates the condition, the propagation distance is broken up into substeps. I'm not sure if I even need to include the time t since I only need a snap shot at one instance in time. The numerical method used is the finite-difference time-domain (FDTD) that has been successfully applied in many engineering fields. Unwrapped phase for tilted plane-wave propagation from under. Now that you’ve looked more closely at the process of sampling and quantization in this chapter, you should have a clearer understanding of the MATLAB and C++ examples in Chapters 2 and 3. I want to use this PWM waveform in an illustration and especially I want to be able to heavily zoom. the purposes from this paper are driving and simulating the propagation of a wave by using Finite Difference Time Domain Modeling Analysis (FDTD), by drive the corresponding FDTD codes from Maxwell's equation and simulate these codes in MATLAB. MATLAB Implementation of a Fourier Approach to Optical Wave Propagation 6. A MATLAB code was written for the wave propagation through the linear elastic material. In general, horizontal polarization represents the worse case for propagation loss due to rain. Text books leave much to be desired regarding visualization of wave propagation since they are not animated. Manolis available from Rakuten Kobo. Seismic Wave Animations: Seismic wave animations for the P, S, Rayleigh and Love waves have been created using a 3-D grid shown in Figure 1. Different type of Wave Plotting using MATLAB 10:05 MATLAB PROGRAMS MATLAB Program: function waves % WAVES Wave equation in one and two space dimensions. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Same function shown with surface normal vectors. This command will plot the elements of vector y (on the. How to plot WAV file. keeping all the parameters constant except time,vary the time and plot the graph for this equation of gaussian wave propagation in a optical fiber. This example shows how a MATLAB m-file can be used to plot a sine wave. 2 Review of Hemispherical Sound Propagation You should recall from Section 5, for a point source in a loss-less medium with no reflections, that the sound intensity is related to power and range by: 2 2 4 ( ). Simulations In Three Dimensions Example. wave optical propagation algorithms each with its specific strengths. Single-file vectorized implementation of acoustic wave propagation in MATLAB. This may sound a bit dumb but how do I plot the hydrogen wave functions? For example, what is exactly being represented [in this image][1]? Is it just the norm-squared of the wave function and is the z-axis sticking out of the page? I'm not sure how to use any other application but I'm using the Mac grapher tool. Simulating the propagation of elastic waves in multi-layered media has many applications. This banner text can have markup. The main functions in the toolbox are the following. MATLAB中文论坛《高等光学仿真(MATLAB)版》——光波导、激光(含第2版)板块发表的帖子:电子书籍分享:Numerical Simulation of Optical Wave Propagation。. It is required to master at least one of the computer languages, e. Choose from 147 different sets of wave propagation flashcards on Quizlet. The calculation technique has been implemented in MATLAB and sample cases are presented for the circular and square piston, as well as a Gaussian- and Bessel-weighted spatial excitation. Key-Words: - Acoustic wave propagation, MATLAB, PE method, Deep waters, Shallow waters 1 Introduction.
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