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Moving Average Filters
CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average filter is optimal for a common task: reducing random noise while retaining a sharp step response. This makes it the premier filter for time domain encoded signals. However, the moving average is the worst filter for frequency domain encoded signals, with little ability to separate one band of frequencies from another. Relatives of the moving average filter include the Gaussian, Blackman, and multiple- pass moving average. These have slightly better performance in the frequency domain, at the expense of increased computation time. Implementation by Convolution As the name implies, the moving average filter operates by averaging a number of points from the input signal to produce each point in the output signal. In equation form, this is written: EQUATION 15-1 Equation of the moving average filter. In M &1 this equation, x[ ] is the input signal, y[ ] is ' 1 % y[i] j x [i j ] the output signal, and M is the number of M j'0 points used in the moving average. This equation only uses points on one side of the output sample being calculated. Where x[ ] is the input signal, y[ ] is the output signal, and M is the number of points in the average. For example, in a 5 point moving average filter, point 80 in the output signal is given by: x [80] % x [81] % x [82] % x [83] % x [84] y [80] ' 5 277 278 The Scientist and Engineer's Guide to Digital Signal Processing As an alternative, the group of points from the input signal can be chosen symmetrically around the output point: x[78] % x[79] % x[80] % x[81] % x[82] y[80] ' 5 This corresponds to changing the summation in Eq. -
Designing Filters Using the Digital Filter Design Toolkit Rahman Jamal, Mike Cerna, John Hanks
NATIONAL Application Note 097 INSTRUMENTS® The Software is the Instrument ® Designing Filters Using the Digital Filter Design Toolkit Rahman Jamal, Mike Cerna, John Hanks Introduction The importance of digital filters is well established. Digital filters, and more generally digital signal processing algorithms, are classified as discrete-time systems. They are commonly implemented on a general purpose computer or on a dedicated digital signal processing (DSP) chip. Due to their well-known advantages, digital filters are often replacing classical analog filters. In this application note, we introduce a new digital filter design and analysis tool implemented in LabVIEW with which developers can graphically design classical IIR and FIR filters, interactively review filter responses, and save filter coefficients. In addition, real-world filter testing can be performed within the digital filter design application using a plug-in data acquisition board. Digital Filter Design Process Digital filters are used in a wide variety of signal processing applications, such as spectrum analysis, digital image processing, and pattern recognition. Digital filters eliminate a number of problems associated with their classical analog counterparts and thus are preferably used in place of analog filters. Digital filters belong to the class of discrete-time LTI (linear time invariant) systems, which are characterized by the properties of causality, recursibility, and stability. They can be characterized in the time domain by their unit-impulse response, and in the transform domain by their transfer function. Obviously, the unit-impulse response sequence of a causal LTI system could be of either finite or infinite duration and this property determines their classification into either finite impulse response (FIR) or infinite impulse response (IIR) system. -
Finite Impulse Response (FIR) Digital Filters (II) Ideal Impulse Response Design Examples Yogananda Isukapalli
Finite Impulse Response (FIR) Digital Filters (II) Ideal Impulse Response Design Examples Yogananda Isukapalli 1 • FIR Filter Design Problem Given H(z) or H(ejw), find filter coefficients {b0, b1, b2, ….. bN-1} which are equal to {h0, h1, h2, ….hN-1} in the case of FIR filters. 1 z-1 z-1 z-1 z-1 x[n] h0 h1 h2 h3 hN-2 hN-1 1 1 1 1 1 y[n] Consider a general (infinite impulse response) definition: ¥ H (z) = å h[n] z-n n=-¥ 2 From complex variable theory, the inverse transform is: 1 n -1 h[n] = ò H (z)z dz 2pj C Where C is a counterclockwise closed contour in the region of convergence of H(z) and encircling the origin of the z-plane • Evaluating H(z) on the unit circle ( z = ejw ) : ¥ H (e jw ) = åh[n]e- jnw n=-¥ 1 p h[n] = ò H (e jw )e jnwdw where dz = jejw dw 2p -p 3 • Design of an ideal low pass FIR digital filter H(ejw) K -2p -p -wc 0 wc p 2p w Find ideal low pass impulse response {h[n]} 1 p h [n] = H (e jw )e jnwdw LP ò 2p -p 1 wc = Ke jnwdw 2p ò -wc Hence K h [n] = sin(nw ) n = 0, ±1, ±2, …. ±¥ LP np c 4 Let K = 1, wc = p/4, n = 0, ±1, …, ±10 The impulse response coefficients are n = 0, h[n] = 0.25 n = ±4, h[n] = 0 = ±1, = 0.225 = ±5, = -0.043 = ±2, = 0.159 = ±6, = -0.053 = ±3, = 0.075 = ±7, = -0.032 n = ±8, h[n] = 0 = ±9, = 0.025 = ±10, = 0.032 5 Non Causal FIR Impulse Response We can make it causal if we shift hLP[n] by 10 units to the right: K h [n] = sin((n -10)w ) LP (n -10)p c n = 0, 1, 2, …. -
Postdoctoral Fellow and Research Engineer Positions
Postdoctoral Fellow and Research Engineer Positions National University of Singapore Principal Investigator: Dr. Yang Liu Email: [email protected]; [email protected]; Homepage:https://www.eng.nus.edu.sg/cee/staff/liu-yang/ 1. Postdoctoral Fellow - 00CUR Description The research project is funded under Artificial Intelligent–Enterprise Digital Platform (AI-EDP) Programme in the areas of Smart City and Smart MRO. The postdoctoral researcher will work in ST Engineering & NUS Joint Lab and collaborate with the Transportation Group in the Department of Civil and Environmental Engineering, the Decision Analysis Group in the Department of Industrial System Engineering and Management, the AI Research group in the Department of Electrical and Computer Engineering at NUS and ST Engineering. The research project aims to develop a methodology framework to generate intelligent traffic diffusion plans and information dissemination strategies by analyzing historical traffic data. It is expected to deliver intelligent tools to access traffic accident impact and to generate traffic diffusion strategies by machine/deep learning, simulation, and optimization techniques. The postdoctoral researcher will lead the research project, supervise research students, and write research proposals and reports. This is a full-time position, and the duration of the first contract is one year. There is an opportunity to extend the position to multiple years, depending on the performance in the first year and the availability of funding. Qualifications • Ph.D. degree -
Automated Annotation of Simulink Generated C Code Based on the Simulink Model
DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020 Automated Annotation of Simulink Generated C Code Based on the Simulink Model SREEYA BASU ROY KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Automated Annotation of Simulink Generated C Code Based on the Simulink Model SREEYA BASU ROY Master in Embedded Systems Date: September 25, 2020 Supervisor: Predrag Filipovikj Examiner: Matthias Becker School of Electrical Engineering and Computer Science Host company: Scania CV AB Swedish title: Automatisk Kommentar av Simulink Genererad C kod Baserad på Simulink Modellen iii Abstract There has been a wave of transformation in the automotive industry in recent years, with most vehicular functions being controlled electron- ically instead of mechanically. This has led to an exponential increase in the complexity of software functions in vehicles, making it essential for manufactures to guarantee their correctness. Traditional software testing is reaching its limits, consequently pushing the automotive in- dustry to explore other forms of quality assurance. One such technique that has been gaining momentum over the years is a set of verification techniques based on mathematical logic called formal verification tech- niques. Although formal techniques have not yet been adopted on a large scale, these methods offer systematic and possibly more exhaus- tive verification of the software under test, since their fundamentals are based on the principles of mathematics. In order to be able to apply formal verification, the system under test must be transformed into a formal model, and a set of proper- ties over such models, which can then be verified using some of the well-established formal verification techniques, such as model check- ing or deductive verification. -
Compiling Maplesim C Code for Simulation in Vissim
Compiling MapleSim C Code for Simulation in VisSim 1 Introduction MapleSim generates ANSI C code from any model. The code contains the differential equations that describe the model dynamics, and a solver. Moreover, the code is royalty-free, and can be used in any simulation tool (or development project) that accepts external code. VisSim is a signal-flow simulation tool with strength in embedded systems programming, real-time data acquisition and OPC. This document will describe the steps required to • Generate C code from a MapleSim model of a DC Motor. The C code will contain a solver. • Implement the C code in a simulation DLL for VisSim. VisSim provides a DLL Wizard that sets up a Visual Studio C project for a simulation DLL. MapleSim code will be copied into this project. After a few modifications, the project will be compiled to a DLL. The DLL can then be used as a block in a VisSim simulation. The techniques demonstrated in this document can used to implement MapleSim code in any other environment. MapleSim’s royalty -free C code can be implemented in other modeling environment s, such as VisSim MapleSim’s C code can also be used in Mathcad 2 API for the Maplesim Code The C code generated by MapleSim contains four significant functions. • SolverSetup(t0, *ic, *u, *p, *y, h, *S) • SolverStep(*u, *S) where SolverStep is EulerStep, RK2Step, RK3Step or RK4Step • SolverUpdate(*u, *p, first, internal, *S) • SolverOutputs(*y, *S) u are the inputs, p are subsystem parameters (i.e. variables defined in a subsystem mask), ic are the initial conditions, y are the outputs, t0 is the initial time, and h is the time step. -
ELEG 5173L Digital Signal Processing Ch. 5 Digital Filters
Department of Electrical Engineering University of Arkansas ELEG 5173L Digital Signal Processing Ch. 5 Digital Filters Dr. Jingxian Wu [email protected] 2 OUTLINE • FIR and IIR Filters • Filter Structures • Analog Filters • FIR Filter Design • IIR Filter Design 3 FIR V.S. IIR • LTI discrete-time system – Difference equation in time domain N M y(n) ak y(n k) bk x(n k) k 1 k 0 – Transfer function in z-domain N M k k Y (z) akY (z)z bk X (z)z k 1 k 0 M k bk z Y (z) k 0 H (z) N X (z) k 1 ak z k 1 4 FIR V.S. IIR • Finite impulse response (FIR) – difference equation in the time domain M y(n) bk x(n k) k 0 – Transfer function in the Z-domain M Y (z) k H (z) bk z X (z) k 0 – Impulse response h(n) [b ,b ,,b ] 0 1 M • The impulse response is of finite length finite impulse response 5 FIR V.S. IIR • Infinite impulse response (IIR) – Difference equation in the time domain N M y(n) ak y(n k) bk x(n k) k1 k0 – Transfer function in the z-domain M k bk z Y(z) k0 H (z) N X (z) k 1 ak z k1 – Impulse response can be obtained through inverse-z transform, and it has infinite length 6 FIR V.S. IIR • Example – Find the impulse response of the following system. Is it a FIR or IIR filter? Is it stable? 1 y(n) y(n 2) x(n) 4 7 FIR V.S. -
Lecture #4: Simulation of Hybrid Systems
Embedded Control Systems Lecture 4 – Spring 2018 Knut Åkesson Modelling of Physcial Systems Model knowledge is stored in books and human minds which computers cannot access “The change of motion is proportional to the motive force impressed “ – Newton Newtons second law of motion: F=m*a Slide from: Open Source Modelica Consortium, Copyright © Equation Based Modelling • Equations were used in the third millennium B.C. • Equality sign was introduced by Robert Recorde in 1557 Newton still wrote text (Principia, vol. 1, 1686) “The change of motion is proportional to the motive force impressed ” Programming languages usually do not allow equations! Slide from: Open Source Modelica Consortium, Copyright © Languages for Equation-based Modelling of Physcial Systems Two widely used tools/languages based on the same ideas Modelica + Open standard + Supported by many different vendors, including open source implementations + Many existing libraries + A plant model in Modelica can be imported into Simulink - Matlab is often used for the control design History: The Modelica design effort was initiated in September 1996 by Hilding Elmqvist from Lund, Sweden. Simscape + Easy integration in the Mathworks tool chain (Simulink/Stateflow/Simscape) - Closed implementation What is Modelica A language for modeling of complex cyber-physical systems • Robotics • Automotive • Aircrafts • Satellites • Power plants • Systems biology Slide from: Open Source Modelica Consortium, Copyright © What is Modelica A language for modeling of complex cyber-physical systems -
Introduction to Simulink
Introduction to Simulink Mariusz Janiak p. 331 C-3, 71 320 26 44 c 2015 Mariusz Janiak All Rights Reserved Contents 1 Introduction 2 Essentials 3 Continuous systems 4 Hardware-in-the-Loop (HIL) Simulation Introduction Simulink is a block diagram environment for multidomain simulation and Model-Based Design. It supports simulation, automatic code generation, and continuous test and verification of embedded systems.1 Graphical editor Customizable block libraries Solvers for modeling and simulating dynamic systems Integrated with Matlab Web page www.mathworks.com 1 The MathWorks, Inc. Introduction Simulink capabilities Building the model (hierarchical subsystems) Simulating the model Analyzing simulation results Managing projects Connecting to hardware Introduction Alternatives to Simulink Xcos (www.scilab.org/en/scilab/features/xcos) OpenModelica (www.openmodelica.org) MapleSim (www.maplesoft.com/products/maplesim) Wolfram SystemModeler (www.wolfram.com/system-modeler) Introduction Model based design with Simulink Modeling and simulation Multidomain dynamic systems Nonlinear systems Continuous-, Discrete-time, Multi-rate systems Plant and controller design Rapidly model what-if scenarios Communicate design ideas Select/Optimize control architecture and parameters Implementation Automatic code generation Rapid prototyping for HIL, SIL Verification and validation Essentials Working with Simulink Launching Simulink Library Browser Finding Blocks Getting Help Context sensitive help Simulink documentation Demo Working with a simple model Changing -
Filename Extensions
Filename Extensions Generated 22 February 1999 from Filex database with 3240 items. ! # $ & ) 0 1 2 3 4 6 7 8 9 @ S Z _ a b c d e f g h i j k l m n o p q r s t u v w x y z ~ • ! .!!! Usually README file # .### Compressed volume file (DoubleSpace) .### Temp file (QTIC) .#24 Printer data file for 24 pin matrix printer (LocoScript) .#gf Font file (MetaFont) .#ib Printer data file (LocoScript) .#sc Printer data file (LocoScript) .#st Standard mode printer definitions (LocoScript) $ .$$$ Temporary file .$$f Database (OS/2) .$$p Notes (OS/2) .$$s Spreadsheet (OS/2) .$00 Pipe file (DOS) .$1 ZX Spectrum file in HOBETA format .$d$ Data (OS/2 Planner) .$db Temporary file (dBASE IV) .$ed Editor temporary file (MS C) .$ln TLink response file (Borland C++) .$o1 Pipe file (DOS) .$vm Virtual manager temporary file (Windows 3.x) & .&&& Temporary file ) .)2( LHA archiver temporary file (LHA) 0 .0 Compressed harddisk data (DoubleSpace) .000 Common filename extension (GEOS) .000 Compressed harddisk data (DoubleSpace) .001 Fax (Hayes JT FAX) (many) .075 75x75 dpi display font (Ventura Publisher) .085 85x85 dpi display font (Ventura Publisher) .091 91x91 dpi display font (Ventura Publisher) .096 96x96 dpi display font (Ventura Publisher) .0b Printer font with lineDraw extended character set (PageMaker) 1 .1 Unformatted manual page (Roff/nroff/troff/groff) .10x Bitmap graphics (Gemini 10x printer graphics file) .123 Data (Lotus123 97) .12m Smartmaster file (Lotus123 97) .15u Printer font with PI font set (PageMaker) .1st Usually README.1ST text 2 .24b Bitmap -
Digital Signal Processing Filter Design
2065-27 Advanced Training Course on FPGA Design and VHDL for Hardware Simulation and Synthesis 26 October - 20 November, 2009 Digital Signal Processing Filter Design Massimiliano Nolich DEEI Facolta' di Ingegneria Universita' degli Studi di Trieste via Valerio, 10, 34127 Trieste Italy Filter design 1 Design considerations: a framework |H(f)| 1 C ıp 1 ıp ıs f 0 fp fs Passband Transition Stopband band The design of a digital filter involves five steps: Specification: The characteristics of the filter often have to be specified in the frequency domain. For example, for frequency selective filters (lowpass, highpass, bandpass, etc.) the specification usually involves tolerance limits as shown above. Coefficient calculation: Approximation methods have to be used to calculate the values hŒk for a FIR implementation, or ak, bk for an IIR implementation. Equivalently, this involves finding a filter which has H.z/ satisfying the requirements. Realisation: This involves converting H.z/ into a suitable filter structure. Block or flow diagrams are often used to depict filter structures, and show the computational procedure for implementing the digital filter. 1 Analysis of finite wordlength effects: In practice one should check that the quantisation used in the implementation does not degrade the performance of the filter to a point where it is unusable. Implementation: The filter is implemented in software or hardware. The criteria for selecting the implementation method involve issues such as real-time performance, complexity, processing requirements, and availability of equipment. 2 Finite impulse response (FIR) filter design A FIR filter is characterised by the equations N 1 yŒn D hŒkxŒn k kXD0 N 1 H.z/ D hŒkzk: kXD0 The following are useful properties of FIR filters: They are always stable — the system function contains no poles. -
FMI Target for Simulink Coder, It Is Now Possible to Export Models from Simulink to Any Platform That Supports Fmus for Co-Simulation
Supporting your vision Cross-Platform Modeling with FMI Target for Simulink® Coder™ Open technology standards for an integrated product lifecycle Engine Transmission Thermal EV/HV Chassis Compo- Models Models Systems Models nents Models Functional Mock-Up Interface The challenge for manufacturers of complex machinery that heavily rely on components from suppliers is the seamless exchange of data and specifications during the development. The same holds true for large corporates with multiple R&D departments at various locations using several development tools due to different objectives. Those challenges include different programming languages from the various tools, the lack of standardized model interfaces and the concerns for the protection of intellectual property. The development of the Functional Mock-up Interface (FMI) has enabled software-, model- and hardware-in-the-loop simulations with dynamic system models from different software environments. With the FMI Target for Simulink Coder, it is now possible to export models from Simulink to any platform that supports FMUs for Co-Simulation. FMI for Co-Simulation The goal is to couple two or more models with solvers in a co-simulation environment. The data exchange between subsystems is restricted to discrete communication points. The subsystems are processed independently from each other by their individual solvers during the time interval between two communication points. Master algorithms control the synchronization of all slave simulation solvers and the data exchange between the subsystems. The interface allows for both standard and advanced master algorithms, such as variable communication step sizes, signal extrapolation of higher order and error checking. FMI Target for Simulink® Coder™ FMI for Co-Simulation For the exchange of models across different platforms, the FMI Target for Simulink Coder enables the export of models from Simulink as FMUs for Co-Simulation.