This doctoral thesis models pulse propagation in optical fibers using finite-difference methods. It summarizes the numerical model, which solves the nonlinear Schrödinger equation describing pulse propagation using Crank-Nicholson and split-step Fourier methods. It tests the model's accuracy by comparing results to analytic solutions and a commercial simulation program. Effects like dispersion, loss, self-phase modulation and polarization mode dispersion are modeled. Additional models are presented for optical amplifiers and filters used in the fiber links.
1. A document describing RC and RL circuits is provided. RC circuits are analyzed using Kirchhoff's laws. The time constant τ is defined as RC. For an RC circuit with an initial voltage V0, the voltage v(t) is given by v(t) = V0e-t/τ.
2. For an RL circuit with an initial current I0, the current i(t) is given by i(t) = I0e-t/τ, where the time constant τ is L/R. Kirchhoff's laws are again used to analyze the RL circuit. The voltage v(t) across the inductor is given by v(t) = RI0
4 matched filters and ambiguity functions for radar signals-2Solo Hermelin
Matched filters (Part 2of 2) maximizes the output signal-to-noise ratio for a known radar signal at a predefined time.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
1. The document discusses transmission lines and their characteristics including different types of transmission lines, distributed circuit models, transmission line equations, and phasor analysis.
2. It also covers topics such as impedance matching, transmission line parameters, wavelength, wave velocity, and signal propagation on transmission lines.
3. Examples of wavelength and wave velocity for different materials at frequencies of 1 GHz and 10 GHz are provided.
This document discusses bipolar junction transistors (BJTs) and their characteristics. It covers topics like PN junctions, current-voltage relationships, exponential current-voltage characteristics of the BJT, and small-signal models including transconductance gm and output resistance rπ. Circuit examples are provided to illustrate concepts like the common emitter amplifier configuration and early effect. Key points covered include the exponential I-V relationship of the BJT, definitions of transconductance and other small-signal parameters, and how the early effect impacts the current-voltage curve.
This document discusses the design of low-noise amplifiers. It begins with an overview of the basic structure of transmitters and receivers in wireless communication systems. It then reviews the relationships between power and gain and introduces the concept of the available power gain circle. The document discusses a design method for amplifiers that does not require simultaneous conjugate matching of both ports. It also covers noise theory for two-port networks and the fixed noise figure circle. The key points are utilizing available power gain circles and fixed noise figure circles to design amplifiers through tradeoffs between gain and noise on the Smith chart.
The document discusses the calculation of magnetic fields generated by electric currents. It begins by defining the Biot-Savart law and provides the formula for calculating the magnetic field generated by a current-carrying wire. It then uses this law to derive integral formulas for the z- and r-components of the magnetic field generated by a long solenoid. It approximates these integrals using a Taylor series expansion to obtain explicit formulas for the magnetic field components as a function of position inside and outside the solenoid. Finally, it presents a graph showing the measured axial magnetic field profile inside a coil carrying a 1A current.
This document discusses traveling waves and scattering parameters for analyzing multi-port networks. It begins by defining traveling waves as voltage and current waves that propagate through transmission lines. It then introduces scattering parameters (S-parameters) which describe the input-output relationship of linear electrical networks with multiple ports. S-parameters are presented as elements of a scattering matrix that relates incoming and outgoing wave amplitudes at each port. Methods for calculating reflection and transmission coefficients from S-parameters are provided for characterizing two-port networks. The analysis is then generalized to n-port networks using scattering matrices. Key parameters like return loss, insertion loss, and available power are defined in terms of S-parameters.
1. A document describing RC and RL circuits is provided. RC circuits are analyzed using Kirchhoff's laws. The time constant τ is defined as RC. For an RC circuit with an initial voltage V0, the voltage v(t) is given by v(t) = V0e-t/τ.
2. For an RL circuit with an initial current I0, the current i(t) is given by i(t) = I0e-t/τ, where the time constant τ is L/R. Kirchhoff's laws are again used to analyze the RL circuit. The voltage v(t) across the inductor is given by v(t) = RI0
4 matched filters and ambiguity functions for radar signals-2Solo Hermelin
Matched filters (Part 2of 2) maximizes the output signal-to-noise ratio for a known radar signal at a predefined time.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
1. The document discusses transmission lines and their characteristics including different types of transmission lines, distributed circuit models, transmission line equations, and phasor analysis.
2. It also covers topics such as impedance matching, transmission line parameters, wavelength, wave velocity, and signal propagation on transmission lines.
3. Examples of wavelength and wave velocity for different materials at frequencies of 1 GHz and 10 GHz are provided.
This document discusses bipolar junction transistors (BJTs) and their characteristics. It covers topics like PN junctions, current-voltage relationships, exponential current-voltage characteristics of the BJT, and small-signal models including transconductance gm and output resistance rπ. Circuit examples are provided to illustrate concepts like the common emitter amplifier configuration and early effect. Key points covered include the exponential I-V relationship of the BJT, definitions of transconductance and other small-signal parameters, and how the early effect impacts the current-voltage curve.
This document discusses the design of low-noise amplifiers. It begins with an overview of the basic structure of transmitters and receivers in wireless communication systems. It then reviews the relationships between power and gain and introduces the concept of the available power gain circle. The document discusses a design method for amplifiers that does not require simultaneous conjugate matching of both ports. It also covers noise theory for two-port networks and the fixed noise figure circle. The key points are utilizing available power gain circles and fixed noise figure circles to design amplifiers through tradeoffs between gain and noise on the Smith chart.
The document discusses the calculation of magnetic fields generated by electric currents. It begins by defining the Biot-Savart law and provides the formula for calculating the magnetic field generated by a current-carrying wire. It then uses this law to derive integral formulas for the z- and r-components of the magnetic field generated by a long solenoid. It approximates these integrals using a Taylor series expansion to obtain explicit formulas for the magnetic field components as a function of position inside and outside the solenoid. Finally, it presents a graph showing the measured axial magnetic field profile inside a coil carrying a 1A current.
This document discusses traveling waves and scattering parameters for analyzing multi-port networks. It begins by defining traveling waves as voltage and current waves that propagate through transmission lines. It then introduces scattering parameters (S-parameters) which describe the input-output relationship of linear electrical networks with multiple ports. S-parameters are presented as elements of a scattering matrix that relates incoming and outgoing wave amplitudes at each port. Methods for calculating reflection and transmission coefficients from S-parameters are provided for characterizing two-port networks. The analysis is then generalized to n-port networks using scattering matrices. Key parameters like return loss, insertion loss, and available power are defined in terms of S-parameters.
This document contains a 24 question multiple choice quiz on electrical engineering concepts. The questions cover topics such as circuit analysis, control systems, power systems, electronics, and digital logic. For each question, the problem statement and several possible answer choices are provided, along with a brief explanation of the correct answer.
Describes Radar Tracking Loops in Range, Doppler and Angles.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://solohermelin.com.
Gate 2013 complete solutions of ec electronics and communication engineeringmanish katara
The document is a sample paper for GATE 2013 that contains 25 multiple choice questions related to engineering topics like logic gates, vector fields, impulse response of systems, diodes, IC technology, and more. Each question is followed by a brief explanation of the answer. The questions cover a range of fundamental concepts in areas like signals and systems, electronics, semiconductor devices, and mathematics.
The document discusses electromagnetic induction in a two-coil system. It presents equations describing the flux linkage and induced voltages in the coils due to changing current. The coils are modeled using inductances L1, L2 and mutual inductance M. Kirchhoff's voltage law is applied to each coil to derive differential equations relating the coil voltages and currents.
The document describes a simulation of an NMOS transistor. It defines the mesh, regions, doping concentrations, materials, and electrical contacts. Initial results are plotted including potential, electric field, and carrier concentrations to analyze the transistor behavior. The gate voltage is then swept to model transistor operation and output current-voltage characteristics.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in closed paths with changing magnetic fluxes.
1) Four positive charges are located at the corners of a square in the xy-plane. A fifth positive charge is located 8cm from the others. The total force on the fifth charge is calculated to be 4.0x10-4 N directed along the z-axis.
2) Two charges of Q1 coulombs are located at z=±1. For a third charge Q2 to produce zero total electric field at (0,1,0), Q2 must lie along the y-axis at y=1±21/4|Q2|/Q1, where the sign depends on the sign of Q2.
3) The total force on a 50nC charge
This document discusses finite difference methods for solving differential equations. It begins by introducing grid-based computation and finite difference approximations of derivatives. It then provides examples of solving differential equations using explicit and implicit finite difference schemes. The document discusses various approaches to implementing finite difference methods in code, including defining the domain, discretization, boundary conditions, and iteration procedures. It also gives examples of applying finite difference methods to problems in math, physics, and heat conduction.
This document contains a sample GATE paper with questions from various subjects like mathematics, physics, chemistry and general aptitude. The questions include multiple choice, numerical answer type and explanation type questions. Some questions test concepts like differential equations, complex numbers, Laplace transforms, electric circuits etc. The document also contains information about an online portal for GATE preparation that has trained over 1 lakh students across India.
The document describes a simulation of an NMOS transistor. It defines the mesh, regions, doping concentrations, materials, and electrical contacts. It then performs the simulation, solving the device at different biases and extracting output parameters and plots.
This document provides an overview of RF transceiver systems and related concepts. It begins with definitions of dB, phasors, and modulation techniques. It then discusses transmitter and receiver architectures, moving from basics to more advanced concepts. Key topics covered include I/Q modulation, linear modulation, transmitter architectures using either I/Q or polar modulation, and the use of phasors in various applications from circuit analysis to communications systems.
The document defines complex frequency as a type of frequency that depends on two parameters: σ, which controls the magnitude of the signal, and w, which controls the rotation. It presents the equation for a complex exponential signal and defines the terms. It then analyzes three cases of complex frequency: 1) when w = 0 and σ varies, 2) when σ = 0 and w varies, and 3) when both σ and w have values. The response of a circuit to various input signals is also analyzed using the complex frequency concept.
This document discusses the finite difference method for solving the neutron transport equation in nuclear reactor analysis. It begins with an overview of neutron transport models and numerical solutions. It then presents the finite difference formulation, including the discretization of derivatives and boundary conditions. Various solution techniques are discussed, such as the Jacobi and Gauss-Seidel iterative methods. Code structure and examples are provided to demonstrate solving the one-dimensional neutron diffusion equation using an explicit finite difference scheme.
This document contains 20 multiple choice questions from a GATE EE exam. It covers topics in signals and systems, circuits, electromagnetic theory, machines, and instrumentation. For each question, the full question and multiple choice options are provided, along with the solution and explanation for the correct answer.
This document summarizes dispersion management in optical fiber communication. It discusses the basic components of an optical fiber including the core, cladding, buffer, and jacket. It also describes optical transmitters such as lasers and LEDs, as well as optical receivers such as photo detectors. The document outlines the main types of dispersion in fibers including material dispersion, waveguide dispersion, and polarization mode dispersion. It compares Gaussian and super Gaussian pulses and how super Gaussian pulses can reduce dispersion, especially at higher data transmission rates. In conclusion, the document provides a basic overview of optical fiber communication and dispersion management techniques.
This document discusses optical fiber communication. It provides a brief history of optical fibers, describing early experiments in the 1870s. It explains the basic components and construction of optical fibers, which use total internal reflection to transmit light signals through a glass core. Applications include cable TV, data transmission, and cellular networks. Advantages are high bandwidth, low signal degradation, and small size. Future uses may include automotive entertainment and connectivity.
This document contains a 24 question multiple choice quiz on electrical engineering concepts. The questions cover topics such as circuit analysis, control systems, power systems, electronics, and digital logic. For each question, the problem statement and several possible answer choices are provided, along with a brief explanation of the correct answer.
Describes Radar Tracking Loops in Range, Doppler and Angles.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://solohermelin.com.
Gate 2013 complete solutions of ec electronics and communication engineeringmanish katara
The document is a sample paper for GATE 2013 that contains 25 multiple choice questions related to engineering topics like logic gates, vector fields, impulse response of systems, diodes, IC technology, and more. Each question is followed by a brief explanation of the answer. The questions cover a range of fundamental concepts in areas like signals and systems, electronics, semiconductor devices, and mathematics.
The document discusses electromagnetic induction in a two-coil system. It presents equations describing the flux linkage and induced voltages in the coils due to changing current. The coils are modeled using inductances L1, L2 and mutual inductance M. Kirchhoff's voltage law is applied to each coil to derive differential equations relating the coil voltages and currents.
The document describes a simulation of an NMOS transistor. It defines the mesh, regions, doping concentrations, materials, and electrical contacts. Initial results are plotted including potential, electric field, and carrier concentrations to analyze the transistor behavior. The gate voltage is then swept to model transistor operation and output current-voltage characteristics.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in closed paths with changing magnetic fluxes.
1) Four positive charges are located at the corners of a square in the xy-plane. A fifth positive charge is located 8cm from the others. The total force on the fifth charge is calculated to be 4.0x10-4 N directed along the z-axis.
2) Two charges of Q1 coulombs are located at z=±1. For a third charge Q2 to produce zero total electric field at (0,1,0), Q2 must lie along the y-axis at y=1±21/4|Q2|/Q1, where the sign depends on the sign of Q2.
3) The total force on a 50nC charge
This document discusses finite difference methods for solving differential equations. It begins by introducing grid-based computation and finite difference approximations of derivatives. It then provides examples of solving differential equations using explicit and implicit finite difference schemes. The document discusses various approaches to implementing finite difference methods in code, including defining the domain, discretization, boundary conditions, and iteration procedures. It also gives examples of applying finite difference methods to problems in math, physics, and heat conduction.
This document contains a sample GATE paper with questions from various subjects like mathematics, physics, chemistry and general aptitude. The questions include multiple choice, numerical answer type and explanation type questions. Some questions test concepts like differential equations, complex numbers, Laplace transforms, electric circuits etc. The document also contains information about an online portal for GATE preparation that has trained over 1 lakh students across India.
The document describes a simulation of an NMOS transistor. It defines the mesh, regions, doping concentrations, materials, and electrical contacts. It then performs the simulation, solving the device at different biases and extracting output parameters and plots.
This document provides an overview of RF transceiver systems and related concepts. It begins with definitions of dB, phasors, and modulation techniques. It then discusses transmitter and receiver architectures, moving from basics to more advanced concepts. Key topics covered include I/Q modulation, linear modulation, transmitter architectures using either I/Q or polar modulation, and the use of phasors in various applications from circuit analysis to communications systems.
The document defines complex frequency as a type of frequency that depends on two parameters: σ, which controls the magnitude of the signal, and w, which controls the rotation. It presents the equation for a complex exponential signal and defines the terms. It then analyzes three cases of complex frequency: 1) when w = 0 and σ varies, 2) when σ = 0 and w varies, and 3) when both σ and w have values. The response of a circuit to various input signals is also analyzed using the complex frequency concept.
This document discusses the finite difference method for solving the neutron transport equation in nuclear reactor analysis. It begins with an overview of neutron transport models and numerical solutions. It then presents the finite difference formulation, including the discretization of derivatives and boundary conditions. Various solution techniques are discussed, such as the Jacobi and Gauss-Seidel iterative methods. Code structure and examples are provided to demonstrate solving the one-dimensional neutron diffusion equation using an explicit finite difference scheme.
This document contains 20 multiple choice questions from a GATE EE exam. It covers topics in signals and systems, circuits, electromagnetic theory, machines, and instrumentation. For each question, the full question and multiple choice options are provided, along with the solution and explanation for the correct answer.
This document summarizes dispersion management in optical fiber communication. It discusses the basic components of an optical fiber including the core, cladding, buffer, and jacket. It also describes optical transmitters such as lasers and LEDs, as well as optical receivers such as photo detectors. The document outlines the main types of dispersion in fibers including material dispersion, waveguide dispersion, and polarization mode dispersion. It compares Gaussian and super Gaussian pulses and how super Gaussian pulses can reduce dispersion, especially at higher data transmission rates. In conclusion, the document provides a basic overview of optical fiber communication and dispersion management techniques.
This document discusses optical fiber communication. It provides a brief history of optical fibers, describing early experiments in the 1870s. It explains the basic components and construction of optical fibers, which use total internal reflection to transmit light signals through a glass core. Applications include cable TV, data transmission, and cellular networks. Advantages are high bandwidth, low signal degradation, and small size. Future uses may include automotive entertainment and connectivity.
This document discusses different types of dispersion in optical fibers, including modal dispersion, material dispersion, waveguide dispersion, and polarization mode dispersion. It defines important terms related to dispersion like group velocity and group delay. It also examines how dispersion causes pulse broadening over distance as different wavelengths within a pulse propagate at different speeds through the fiber. Finally, it compares the dispersion characteristics of different fiber types like dispersion shifted and flattened fibers which are designed to reduce dispersion effects.
This document provides an introduction to fiber optics and light propagation in an optical communication lecture. It defines an optical waveguide as a physical structure that guides electromagnetic waves in the optical spectrum. Common types are optical fiber and rectangular waveguides. Optical fiber consists of a core with a high refractive index surrounded by cladding with a lower refractive index and an outer protective jacket. Light is guided down the fiber through total internal reflection at the core-cladding boundary. Fibers can be single-mode, carrying a single ray of light, or multi-mode, carrying multiple light rays concurrently through the core.
Dispersion Compensation Techniques for Optical Fiber CommunicationAmit Raikar
This document discusses dispersion in optical fiber communication systems and various techniques to compensate for it, including dispersion compensating fibers, fiber Bragg gratings, electronic dispersion compensation, digital filters, and optical phase conjugation. Dispersion increases pulse spreading and affects signal quality. These techniques help reduce dispersion to improve transmission over long distances. The document compares the advantages and disadvantages of each technique.
Losses in optical fibers include attenuation from absorption and scattering, as well as dispersion effects. Attenuation is caused by absorption of light energy through heating of impurities in the fiber, resulting in a loss of optical power over length. Dispersion causes pulse broadening and occurs from intermodal and intramodal effects such as material and waveguide dispersion. An optical time domain reflectometer (OTDR) can be used to detect faults, splices, and bends in fibers by emitting light pulses and measuring backscattered light over time to map reflections in the fiber.
application of fibre optics in communicationRimmi07
Fibre optic communication has revolutionised telecommunications by enabling much longer distance links with lower loss and higher data rates. Fibre optic systems use total internal reflection to transmit light through the fibre and are used widely in telecom backbones, broadband networks, and data transmission. Single mode fibre has a small core and transmits single signals for long distances, while multi-mode fibre has a larger core and transmits multiple signals for shorter links like local networks. Fibre optics enable high-speed internet, cable TV, and reliable data transmission.
Optical fiber is a flexible transparent fiber made of high quality glass or plastic that transmits light between two ends. It functions as a waveguide or light pipe. Optical fibers are widely used for fiber optic communications due to their ability to transmit signals over longer distances and higher bandwidths compared to other forms of communication. Fibers are used instead of metal wires because signals travel along them with less loss and are safe from electromagnetic interference. Optical fibers have been used for communication since the 1840s and are now used for transmitting data at rates as high as 400 gigabits per second. Optical fiber provides benefits such as greater bandwidth, immunity to electrical interference, and lower signal attenuation over long distances compared to conventional copper cables.
This document provides an overview of optical fiber communication. It begins with introducing optical fibers and how they guide light through total internal reflection. It then describes the different types of optical fibers, including step index and graded index fibers. The key elements of an optical fiber communication system are presented, along with the benefits such as high bandwidth, low loss, and electrical isolation. Applications include telecommunications networks, computing, and military systems. In conclusion, while optical fibers have some disadvantages, they have revolutionized communications due to their wide bandwidth and low transmission losses.
This document discusses optical waveguides and optical fibers. It covers their classification by geometry and mode structure, as well as by refractive index distribution. It also discusses how purification of materials has allowed optical fiber losses to decrease from over 1000 dB/km initially to below 0.2 dB/km currently. Total internal reflection is described as the mechanism that allows light propagation in optical fibers. Acceptance angle and numerical aperture are also defined as they relate to light entering and propagating within an optical fiber.
This document provides an overview of optical fibers, including their evolution, structure, working principles, classification, communication systems, advantages and applications. It discusses how optical fibers guide light using total internal reflection. Fibers are classified based on mode (single or multi-mode) and refractive index profile (step or graded). Key advantages are high bandwidth, low attenuation, immunity to EMI, and security. Applications include telecommunications, broadband, medicine, military and more. Optical fibers have become the backbone of long-distance networks since the 1980s due to refinements in manufacturing.
We have implemented a multiple precision ODE solver based on high-order fully implicit Runge-Kutta(IRK) methods. This ODE solver uses any order Gauss type formulas, and can be accelerated by using (1) MPFR as multiple precision floating-point arithmetic library, (2) real tridiagonalization supported in SPARK3, of linear equations to be solved in simplified Newton method as inner iteration, (3) mixed precision iterative refinement method\cite{mixed_prec_iterative_ref}, (4) parallelization with OpenMP, and (5) embedded formulas for IRK methods. In this talk, we describe the reason why we adopt such accelerations, and show the efficiency of the ODE solver through numerical experiments such as Kuramoto-Sivashinsky equation.
This document summarizes the design of microwave filters using composite, m-derived, T-network, and π-network sections. It describes:
1) How constant-k sections have very slow attenuation rates and non-constant image impedances. M-derived sections are introduced to address this by replacing component values to obtain the same image impedance as the constant-k section.
2) The propagation constant and image impedance equations for low-pass and high-pass T-network and π-network constant-k and m-derived sections.
3) Composite filters formed by combining m-derived and constant-k sections act as proper filters with rapid initial attenuation that does not reduce at higher
OPTIMIZED RATE ALLOCATION OF HYPERSPECTRAL IMAGES IN COMPRESSED DOMAIN USING ...Pioneer Natural Resources
This document discusses optimizing the rate allocation of hyperspectral images compressed using JPEG2000. It presents a mixed model for bit allocation that combines high and low bit rate models. This mixed model and an optimal rate allocation approach based on minimizing mean squared error under a rate constraint provide lower reconstruction errors than traditional approaches. Computational tests on hyperspectral data show the discrete wavelet transform allows for faster processing and less memory usage compared to the Karhunen-Loeve transform.
Identification of the Mathematical Models of Complex Relaxation Processes in ...Vladimir Bakhrushin
The approach to solving the problem of complex relaxation spectra is presented.
Presentation for the XI International Conference on Defect interaction and anelastic phenomena in solids. Tula, 2007.
1) The document introduces concepts related to high frequency electronic circuits and communication systems, including dB definitions, phasors, modulation, linear modulation and transmitters.
2) It discusses phasor representation in the complex plane and how phasors can represent sinusoidal signals.
3) It covers various modulation techniques including amplitude modulation, frequency modulation, phase modulation, and linear modulation. Linear modulation uses an in-phase (I) component and quadrature (Q) component to modulate the carrier signal.
This document discusses discrete-time signals and systems. It defines discrete-time signals as continuous-amplitude signals that are represented by a discrete sequence of values obtained through sampling a continuous-time signal. Linear time-invariant systems are introduced as systems where the output is the input convolved with the system's impulse response. Examples of discrete-time signals and systems are provided to illustrate concepts such as shifting signals by adding or subtracting from the time index n.
This document summarizes several receiver architectures including superheterodyne, direct conversion, and Weaver. It describes the complex baseband representation of bandpass signals and how orthogonality of the I and Q signals allows doubling of bandwidth. Issues like image rejection, gain/phase imbalance, and half-IF interference are discussed for different architectures. The Hilbert architecture and Weaver architecture are presented as ways to implement direct conversion receivers with improved image rejection compared to traditional methods.
dynamical analysis of soil and structuresHaHoangJR
1. The document discusses various topics in dynamics and vibrations including earthquake engineering, blast engineering, wind engineering, dynamic foundation design, pile driving, offshore foundations, geophysical methods, and dynamic design of transportation systems.
2. It introduces basic principles of dynamics and vibrations including Newton's laws of motion. It describes discrete systems with a finite number of degrees of freedom and continuous systems with infinite degrees of freedom.
3. The analysis of a single degree of freedom system is presented, including deriving the equation of motion and discussing free and forced vibration problems. Solutions are provided for different damping conditions.
The document discusses the design of finite impulse response (FIR) filters. It outlines the main steps in FIR filter design as specifying requirements, calculating coefficients, realizing the filter structure, analyzing word length effects, and implementing the filter. It then focuses on calculating filter coefficients using the window method and examples. The window method involves specifying the desired frequency response, obtaining the impulse response, selecting a window function, and determining coefficients by multiplying the impulse response by the window function. Common window functions like Hamming, Kaiser and their properties are also covered.
(1) The document discusses obtaining first-order low-pass, high-pass, band-reject, and band-pass filters from a first-order all-pass filter.
(2) It shows how to derive the transfer functions for each filter type by adding or subtracting the input and output of one or two cascaded all-pass filter sections.
(3) Key specifications of each filter like cutoff frequencies, gain, and bandwidth are calculated and verified through SPICE simulation, showing good agreement between calculated and simulated responses.
Phase diagram at finite T & Mu in strong coupling limit of lattice QCDBenjamin Jaedon Choi
This document summarizes the derivation of an effective free energy for QCD at strong coupling using a mean field approximation with 1 flavor staggered fermion. Key steps include:
1) Performing a path integral over spatial link variables to obtain quark propagators.
2) Introducing auxiliary bosonic fields using a Hubbard-Stratonovich transformation to obtain a bilinear form in quark fields.
3) Applying a mean field approximation to the auxiliary fields.
4) Exactly integrating over temporal links, quark and auxiliary baryon fields to obtain an effective free energy in terms of the auxiliary meson field.
5) Analyzing the effective free energy to determine the QCD phase diagram as functions of temperature and
This document proposes a technique called Differential Distributed Space-Time Coding OFDM (D-DSTC OFDM) to address synchronization issues in asynchronous cooperative relay networks. It discusses how conventional distributed space-time coding suffers from inter-symbol interference due to relay synchronization errors. The proposed D-DSTC OFDM approach uses differential encoding, circular time reversal, and OFDM modulation to eliminate the need for channel state information or strict relay synchronization. Simulation results show the BER performance of D-DSTC OFDM degrades gracefully with increasing synchronization errors, outperforming coherent detection schemes. The key advantages and limitations of the D-DSTC OFDM approach are summarized.
Here are the key steps to solve this problem:
1. Calculate the coefficient of variation for each factory:
Factory A:
Coefficient of variation = Standard deviation/Average
= 6.5/19.7 = 33%
Factory B:
Coefficient of variation = Standard deviation/Average
= 8.64/21 = 41%
2. The factory with the lower coefficient of variation has more consistent profits.
Factory A has a coefficient of variation of 33%, lower than Factory B's 41%. Therefore, the profits of Factory A are more consistent.
The coefficient of variation allows us to compare the extent of variability in relation to the average of the data set. A lower coefficient
1. The document discusses various topics related to waves including reflection, refraction, interference, diffraction, and standing waves.
2. Reflection can be of two types - closed or fixed end reflection where the phase changes by 180 degrees, and open or free end reflection where the phase does not change.
3. Refraction follows Snell's law where the ratio of sines of the angles of incidence and refraction is equal to the ratio of phase velocities in the two media. Refraction occurs when waves move from a deep to shallow region or vice versa.
1. The document discusses various topics related to waves including reflection, refraction, interference, diffraction, and standing waves.
2. Reflection can be of two types - closed or fixed end reflection where the phase changes by 180 degrees, and open or free end reflection where the phase does not change.
3. Refraction follows Snell's law where the ratio of sines of the angles of incidence and refraction is equal to the ratio of phase velocities in the two media. Refraction occurs when waves move from a deep to shallow region or vice versa.
This document discusses various measures of dispersion used to quantify the spread or variability in data. It defines absolute and relative measures of dispersion and describes key measures such as range, interquartile range, mean deviation, standard deviation, and coefficient of variation. Examples are provided to demonstrate calculating these measures from data sets. The standard deviation is identified as the most common measure of dispersion and its properties are outlined.
The document discusses modeling dynamic systems and earthquake response. It covers basic concepts like Fourier transforms, single and multi-degree of freedom systems, modal analysis, and elastic response spectra. Numerical methods are presented for dynamic analysis in the frequency and time domains, including the finite element method and method of complex response. Examples of earthquake records, harmonic motion, and Fourier transforms are shown.
The document discusses modeling dynamic systems and earthquake response. It covers basic concepts like Fourier transforms, single and multi-degree of freedom systems, modal analysis, and elastic response spectra. Numerical methods are presented for dynamic analysis in the frequency and time domains, including the finite element method and method of complex response. Examples of earthquake records and harmonic motion are shown.
The document discusses modeling dynamic systems and earthquake response. It covers basic concepts like Fourier transforms, single and multi-degree of freedom systems, modal analysis, and elastic response spectra. Numerical methods are presented for dynamic analysis in the frequency and time domains, including the finite element method and method of complex response. Examples of earthquake records and harmonic motion are shown.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!SOFTTECHHUB
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Ph ddefence
1. University of Zagreb
Faculty of Electrical Engineering and Computing
Analysis of Signal Propagation in
Optical Fiber Based on
Finite - Difference Method
Sonja Zentner Pilinsky
Doctoral Thesis, Zagreb, 2003
2. 2
Contents:
1. Introduction
2. Pulse propagation in optical fiber
3. Numerical model and its accuracy
4. Selected simulation results
5. Conclusions
4. 4
Motivation
- need for accurate program with all effects included:
new sophisticated optical links
upgrade of existing fiber links
- expensive experiments
why to model optical link
- linear fiber communications at the edge (bit rates, capacity)
- optical transmission very sensitive to:
dispersion (cromatic, polarization mode)
loss
nonlinear effects
noise
5. 5
Goal - to model modern optical links
dispersion map
6. 6
What we model
Nonlinear Schrödinger equation (NLSE)
0
2
2 2
ω=ω
β
β =
ω
d
d
nonlinear coeff.
describing SPM
fiber loss in dB/km
time
1
1
gv
β =
distance along fiber
optical pulse
complex envelope
2 0ω
γ =
eff
n
cA
7. 7
How we model
- FDM → Cranck - Nicholson
- pseudospectral → SSFM
- testing accuracy on canonical problems
- comparison with OptiSystem 2.0.
Models for additional devices
- EDFA model (G, ASE noise)
- Optical filter model (transfer function)
9. 9
Maxwell equations
0
f
t
t
∂
∇ × = −
∂
∂
∇ × = +
∂
∇ ⋅ = ρ
∇ ⋅ =
f
B
E
D
H J
D
B
0
0
= ε +
= µ +
D E P
B H M
Optical fiber:
-no sources Jf ,ρf = 0
-nonmag.mat M = 0
( ) ( )
( ) ( )1
0, ,L t t t t dt
∝
−∝
′ ′ ′= ε χ − ⋅∫P r E r
( ) ( )
( ) ( ) ( ) ( )3
0 1 2 3 1 2 3 1 2 3, , , , , ,NL ijklt t t t t t t t t t dt dt dt
∝ ∝ ∝
−∝ −∝ −∝
= ε χ − − −∫ ∫ ∫P r E r E r E r
10. 10
Assumption and approximation:
( ) ( ) 2
/∇ ∇ ⋅ = ∇ ⋅∇ε ε << ∇E E E
( ) 2 2
∇ × ∇ × = ∇ ∇ ⋅ − ∇ ≈ −∇E E E E
WGA ∆ ≈ (ncore – ncladding)/ ncore << 1
- the EM field maintains its polarization along the fiber
- Weakly guiding approximation
11. 11
- PNL is treated as a small perturbation to PL
- nonlinear effects: Kerr and Raman (neglected for T0 > 1ps)
instantaneous
response
( )
( ) ( )
( ) ( ) ( )3 3
1 2 3 1 2 3, ,ijkl t t t t t t t t t t t tχ − − − = χ δ − δ − δ −
- SVEA - slowly varying envelope approximation
- envelope is slowly varying in z and t
- removes backscattered part of the envelope
( )0 , 1 L NLk
c
ω
= ε ω = + ε + ε
( ) ( ) ( )
( )
23
0
3
, , , ,
4
NL NL NLP t E t E t= ε ε ε = χr r r
12. 12
( )
( )
( )
2
2
32 0 0
4
,
2 3
,
8
,
I
xxxx eff
eff eff
F x y dxdy
n k Z
A
A n cA
F x y dxdy
∝ ∝
−∝ −∝
∝ ∝
−∝ −∝
ω γ = = χ =
∫ ∫
∫ ∫
Propagation equation for pulse complex envelope:
SVEA assumption: ° ( ) ( ) ° ( ) 0
0 0, , , ej z
E F x y A z β
ω − ω = ω − ωr
HE11 mode ( )
( )
( ) ( )
0
0
,
,
,
a
J a
F x y a
J a e a
−γ ρ−
κρ ρ ≤
=
κ ρ ≥
ρ
13. 13
- α [dB/km]=-10log-α[1/km]
- absorption (intrinsic and extrinsic)
- scattering - linear: Rayleigh and Mie
- nonlinear: Raman and Brillouin
Fiber loss:
14. 14
- caused by material and waveguide dispersion
- mathematically described by
( ) ( ) ( ) ( ) ( )
2 3
0 1 0 2 0 3 0
1 1
..
2 3!
.
ω
β ω = ω = β +β ω− ω + β ω− ω + β ω− ω +n
c
1
1 ps
km
g
g
n
c v
β = =
( ) ( )
0 0
2 23 2
0
2 2 2 2
ps
2
d n d n
c d c d kmω=ω λ=λ
ω λ ω λ
β ≈ ≈
ω π λ
( ) ( )
0 0
2 3 3
3 02 3
1 ps
3
km
d n d n
c d dω=ω ω=ω
ω ω
β = + ω
ω ω
2
0
2
D
T
L =
β
3
0
3
D
T
L′ =
β
Group velocity
dispersion:
15. 15
( ) ( )
2
2
2,
2
I
E
n E n n
Z
ω = ω +Kerr effect
SPM
XPM
FWM
2 0 2 0 1
Wkm
I I
eff eff
n k n
A cA
ω
γ = =
SPM without dispersion:
2
00
,
1
,
z
NL
NL
U j
e U U
z L
A
U L
PP
−α∂
=
∂
= =
γ
Self Phase
Modulation:
( ) ( ) ( )0 2
2 2 I
n z n I t z
π π
Φ = ω + Φ + ω ⋅
λ λ
( ) ( ) ( )
( ) ( )
,
2
, 0,
1
, 0, ,
NLi z T
z
eff
NL eff
NL
U z T U T e
z e
z T U T z
L
Φ
−α
=
−
Φ = =
α
16. 16
Polarization mode dispersion
- caused by circular asymmetries in the fiber
- locally birefringence
2
x y
x y
n
c c
n n
ω ω π
∆β = β − β = − = ∆
λ 1 1
2
B
x y
L
n
λ π
= =
∆ β − β
- measure of pulse splitting in biref. fiber - DGD
g
L d n d n
L L
v d c c d
∆β ∆ ω ∆
∆τ = = = +
∆ ω ω
17. 17
2
22
2 2
2
2 2
2 2
2
2 2 2 3
2
2 2 2 3
x x x
x x y x
y y y
y y x y
A A Aj
A j A A A
z t t
A A Aj
A j A A A
z t t
∂ ∂ ∂∆β α
+ + β + = γ +
∂ ∂ ∂
∂ ∂ ∂∆β α − + β + = γ + ∂ ∂ ∂
PMD (cont.)
- alternative method for linear optical element
( ) ( )
( ) ( )
,out in
a b
b a∗ ∗
ω ω
= ⋅ =
− ω ω
J A J A
0
00
2 2
0 0 0
1
x
y
j
xx
j
y y
x y
a eE
EE a e
E E E
φ
φ
= =
= +
J
DGD ( ) ( ) ( )
2 2
2 a b′ ′∆τ ω = ω + ω a’(ω) ≈ [a(ω+∆ω) – a(ω)] / ∆ω
- globally - birefringence combined with random
polarization mode coupling:
18. 18
3. Numerical model and its accuracy
♦FDM or SSFM ?
♦Accuracy check and comparison with
OptiSystem 2.0
♦EDFA model and filter model
20. 20
- solving numerical scheme to prescribed initial values
and boundary conditions
- errors: modeling, truncation, round-off
FDM steps
- dividing solution region into a grid of nodes
- PDE → finite difference equivalent (numerical stability!!)
21. 21
Derivative Finite difference approximation Type Error
1i i
t
+ψ −ψ
∆
FD O(∆t)
1i i
t
+ψ −ψ
∆
BD O(∆t)
1 1
2
i i
t
+ −ψ −ψ
∆
CD O(∆t2
)
2 14 3
2
i i i
t
+ +−ψ + ψ − ψ
∆
FD O(∆t2
)
1 23 4
2
i i i
t
− −ψ − ψ +ψ
∆
BD O(∆t2
)
t
′ψ
2 1 1 28 8
12
i i i i
t
+ + − −−ψ + ψ − ψ +ψ
∆
CD O(∆t4
)
( )
2 1
2
2i i i
t
+ +ψ − ψ +ψ
∆
FD O(∆t2
)
( )
1 2
2
2i i i
t
− −ψ − ψ +ψ
∆
BD O(∆t2
)
( )
2 1
2
2i i i
t
+ −ψ − ψ + ψ
∆
CD O(∆t2
)
tt
′′ψ
( )
2 1 1 2
2
16 30 16i i i i i
t
+ + − −−ψ + ψ − ψ + ψ −ψ
∆
CD O(∆t4
)
Accuracy
22. 22
2
2
.
A A
const
z t
∂ ∂
=
∂ ∂
First order (Euler)
( )
1 1
1
2
2
. i i
n n nn n
ii i
const
z t
+ −
+
ψ − ψ + ψψ − ψ
=
∆ ∆
- one step, explicit, unstable
( ) ( )
11 1 11 1
1 1 11
2 2
2 2.
2
i i i i
n n n n n nn n
i ii i const
z t t
+ − + −
+ + ++ ψ − ψ + ψ ψ − ψ + ψψ − ψ
= +
∆ ∆ ∆
Crank-Nicholson
- one step, implicit, accurate (1 in z, 2 in t), uncond. stable
( )
1 1
1 1
2
2
.
2
i i
n n nn n
ii i
const
z t
+ −
+ −
ψ − ψ + ψψ − ψ
=
∆ ∆
Leapfrog
- two step, explicit, accurate (2 in z, 2 in t), always unstable
Dufort-Frankel
( )
1 1
1 11 1
2
.
2
i i
n n n nn n
i ii i
const
z t
+ −
+ −+ − ψ − ψ − ψ + ψψ − ψ
=
∆ ∆
- two step, explicit, accurate (2 in z, 2 in t), uncond. stable
Various FDM schemes for eq.
23. 23
Accuracy
1. comparison with analytic solutions for simple problems
2. Comparison with simulations obtained by OptiSystem 2.0
( )
( ) ( )
1
1 1
NM
NM ex
i i
i
NM NM
NM NM ex ex
i i i i
i i
AKC a jb
∗
=
∗ ∗
= =
ψ ψ
= = +
ψ ψ ⋅ ψ ψ
∑
∑ ∑
1
1 NMAX
ex ZMAX
i i
i
ER
NMAX =
= ψ − ψ∑
2
1
1 NM
ex NM
i i
i
SER
NM =
= ψ − ψ∑
Mean error Mean square error
Correlation coefficient
( )
2 2
arg
AKC a b
b
AKC arctg
a
= +
=
Measure of accuracy:
24. 24
M E A N T I M E E R R O R = 2 . 7 1 8 7 0 2 5 7 4 3 9 6 3 5 9 E - 0 0 5
S Q U A R E M T E = 3 . 1 8 8 2 5 1 6 8 9 5 9 1 3 0 2 E - 0 0 9
A U T O C O R R E L A T I O N = 0 . 9 9 9 9 9 7 6 1 3 9 7 3 6 2 8 - j 1 . 3 3 4 9 1 6 9 4 5 0 6 8 7 2 8 E - 0 0 5
| A K C | = 0 . 9 9 9 9 9 7 6 1 4 0 6 2 7 2 9 a r g ( A K C ) = - 7 . 6 4 8 5 2 8 9 4 4 4 3 0 9 6 7 E - 0 0 4
Gaussian pulse
( )
2
2
02
00,
T
T
A T A e
−
=
( ) ( )
2
0
2
0 220
0 2
0 2
,
T
T j zT
A z T A e
T j z
−
− β
=
− β
Analytic solution:
Input pulse:
FDM:
ER = 1.77E-004
SER = 1.36E-007
1-|AKC| = 3.8E-005
arg (AKC)= 7E-004°
SSFM:
ER = 1.88E-004
SER = 1.56E-007
1-|AKC| = 4.4E-005
arg (AKC)= 2.75E-003°
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
1
26
51
76
101
126
151
176
201
226
251
276
301
326
351
376
401
426
451
476
501
number of points in time window
pulsepower[W]
analytic solution
OptiSystem
FiberProp
Input
pulse
fiber
A0 = 0.01 W1/2
α= 0
T0 = 40 ps D = 16 ps/kmnm
λ0 = 1550 nm γ = 0
25. 25
Hyperbolic secant pulse:
2
2
2 2
2 2
A j A
A j A A
z T
∂ ∂ α
+ β + = γ
∂ ∂
2
2 0 0
0 20
, , , D
D NL
PTLA z T
U N
L T LP
γ
= ξ = τ = = =
β
2
22
2 2
sgn
2
U j U
jN U U
∂ ∂
+ β =
∂ξ ∂τ
( ) ( )0, sechu Nτ = τ ( ) ( ) 2
, sech
j
u e
ξ
ξ τ = τ
input pulse analytic solution
input pulse fiber
P0 = 22.6 mW α= 0
T0 = 2.7 ps β2 = -0.243 ps2
/km
λ0 = 1552 nm γ= 1.475 W-1
km-1
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0 100 200 300 400 500
number of points in time window
analyticvalue-computersimul.
FiberProp
OptiSystem
normalization:
26. 26
-3.00E-03
-2.00E-03
-1.00E-03
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-03
0 100 200 300 400 500 600
number of points in time window
analyticsolution-progr.simulation
OptiSystem
FiberProp
Second order soliton pulse: input pulse
analytic solution
( ) ( )0, sechu Nτ = τ
( )
( ) ( )
( ) ( ) ( )
4
2
2cosh 3 6cosh
, 2
cosh 4 4cosh 2 3cos 4
j
j T T e
U T e
T T
ξξ
+
ξ =
+ + ξ
input pulse fiber
P0 = 90.4 mW α= 0
T0 = 2.7 ps β2 = -0.243 ps2
/km
λ0 = 1552 nm γ= 1.475 W-1
km-1
2
0
0
22 2
D
T
z L
π π
= =
β
L = 2z0 = 94.25 km
27. 27
-8.00E-03
-6.00E-03
-4.00E-03
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
0 100 200 300 400 500
number of points in time window
analyticalsolution-progr.simulation
OptiSystem
FiberProp
Third order soliton pulse: input pulse
analytic
solution
( ) ( )0, sechu Nτ = τ
L = 5z0 = 235.67 km
( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
4
2
12 8 8 16
2cosh 8 32cosh 2 36cosh 4 16cosh 6
, 3
cosh 9 9cosh 7 64cosh 3 36cosh
20cosh 4 80cosh 2 5 45 20
36cosh 5 cos 4 20cosh 3 cos 12 90cosh cos 8
j
j
j j j j
T T T T e
U T e
T T T T
T T e e e e
T T T
ξξ
ξ −− ξ ξ ξ
+ + + + ξ =
+ + + +
+ + + +
ξ + ξ + ξ
N = 3
P0 = 203.4 mW
28. 28
4th order soliton pulse - NO analytic solution:
N = 4
P0 = 361.56 mW
L = 2z0 = 94.25 km
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 33 65 97 129 161 193 225 257 289 321 353 385 417 449 481
number of points in time window
pulsepower[W]
FiberProp
OptiSystem
30. 30
Filter model
( )
2
0
1 2
1
2
f f
B
− −
( )0
1
1 cos
2
f f
B
π
+ −
( ) ( )
2
0
2
exp ln 2 f f
B
− −
( )
2
0
1
2
1 f f
B
+ −
Parabolic – shape characteristic
Cosine – shape characteristic
Lorentzian – shape characteristic
Gaussian – shape characteristic
Fabry-Perot
filter !!!
31. 31
B
B S
ω 0 f r e q u e n c y
f i l t e r t r a n s f e r f u n c t i o n
s o l i t o n s p e c t r u m
Why are filters used in nonlinear optical links?
• compensation of Gordon-Haus effect
• filtering at the receivers end
Filter model (cont.)
32. 32
4. Selected simulation results
♦FiberProp and its abilities
♦High bit rates soliton systems
♦Gordon-Haus effect and its compensation
♦Dispersion-compensated and
dispersion-managed systems
♦Polarization dispersion
♦Dispersion compensated system
45. 45
Conclusions:
♦The derivation of optical pulse propagation equation is given
in details. All important effects influencing pulse propagation
in optical fiber are analyzed: fiber loss, cromatic dispersion,
polarization mode dispersion, nonlinear effects (especially
self-phase modulation)
♦Several numerical models are analyzed and the most
accurate one chosen for propagation equation modeling.
The accuracy is tested on simple canonical problems and
later on compared with commercially available software.
♦EDFA model strictly in time domain is developed, with
special attention given to ASE noise model. EDFA model and
optical filter model are included in computer program
FiberProp
46. 46
♦ The new approach to Gordon-Haus limitation derivation is
given. Timing jitter due to Gordon-Haus effect and its
suppression was analyzed with the FiberProp computer
program.
♦ Numerous examples of soliton and dispersion-managed
soliton transmission systems are analyzed and guidelines
for their design are given.
Conclusions (cont.):