DSP First. Laboratory Exercise #10. The z, n, and ˆω Domains
|
|
- Abner Jacobs
- 5 years ago
- Views:
Transcription
1 DSP First Laboratory Exercise #10 The z, n, and ˆω Domains 1 Objective The objective for this lab is to build an intuitive understanding of the relationship between the location of poles and zeros in the z-domain, the impulse response h[n] in the ndomain, and the frequency response H(e j ˆω ) (the ˆω domain). A graphical user interface (GUI) called pez was written in Matlab for doing interactive explorations of the three domains. 1 2 Warm-up Invoke pez by simply typing pez at the Matlab prompt, if you have the DSP First Toolbox installed. A control panel with a few buttons and a plot of the unit circle in the complex z-plane will pop up. You can use the controller to selectively place poles and zeros in the z-plane, and then observe how their placement affects the impulse and frequency responses. If the plots need manual updating, click on the Redo Plots button under <Quicksize...> menu. The Real Time Drag Plots button will put pez in a mode such that an individual pole/zero (pair) can be moved around and the corresponding H(e j ˆω ) and h[n] plots will be updated. Since exact placement of poles and zeros with the mouse is difficult, an Edit By Co-Ord button is provided for numerical entry of the real and imaginary parts, or magnitude and angle (a separate edit window will appear when you use this option). Before you can edit a pole or zero, however, you must first select it with the mouse. Removal of individual poles or zeros can also be performed by clicking on the Delete Poles & Zeros (again, a separate window will appear). Note that all poles and/or zeros can be easily cleared by clicking on the <Clear...> menu, and then selecting Poles, Zeros, orall. Play around with pez for a few minutes to gain some familiarity with the interface. Try implementing a 3-point averager by placing its zeros (and poles) at the correct location in the z-plane. Instructor Verification (separate page) PEZ CD-ROM 3 Laboratory: Relationships between z, n, and ˆω domains Work through the following exercises and keep track of your observations by filling in the worksheet at the end of this assignment. In general, you want to make note of the following quantities: How does h[n] change with respect to oscillation period and rate of decay? How does H(e j ˆω ) change with respect to peak location and width. 4 Real Poles (a) Use pez to place a pole at z = 1 2. You may have to use the Edit by Co-Ord button to get the location exactly right. Use the plots for this case as the reference for answering the next 1 pez was written by Craig Ulmer. CD-ROM Instructor Verification Sheet 1
2 four parts. (b) Move the pole close to the origin (still on the real axis). You can do this by clicking on the pole and dragging it to the new location. Describe the changes in the impulse response h[n] and the frequency response H(e j ˆω ). (c) You can also move poles and zeros under the influence of the Real Time Drag Plots option in pez. When this box is checked, the impulse response and frequency response plots are updated while you move the pole (or zero). Once this mode is set, click on the pole you want to move and start to drag it slowly. Watch for the update of the plots in the secondary window. After the real-time updating has started, you can release the mouse button and the pole (or zero) will follow the cursor. Click on the pole once more to stop moving it and to stop the updating. It is sometimes a little tricky to use. Also the display may be jerky unless you have a high-performance computer with fast graphics. Move the real pole slowly from z = 1 2 to z = 1 and observe the changes in the impulse response h[n] and the frequency response H(e j ˆω ). (d) Place the pole exactly on the unit circle. Describe the changes in h[n] and H(e j ˆω ). (e) Move the pole outside the unit circle. Describe the changes in h[n] and H(e j ˆω ). (f) In general, where should poles be placed to guarantee system stability? By stability we mean that the system s output does not blow up. 5 Complex Poles If the denominator polynomial A(z) has a complex root, it will have a second root at the conjugate location when the polynomial coefficients are real. For example, if we place a root at z = j 1 2, then we will also get one at z = 1 3 j 1 2. (a) What property of the polynomial coefficients of A(z) =1+a 1 z 1 +a 2 z 2 will guarantee that the roots come in conjugate pairs? (b) Clear all the poles and zeros from pez. Now place a pole with magnitude 0.75 at an angle of 45 ; and then two zeros at the origin. Note that pez automatically places a conjugate pole in the z-domain. (c) Derive the filter coefficients for the denominator A(z) and numerator B(z) =b 0 +b 1 z 1 + b 2 z 2. Use the following relationship: B(z) A(z) = G (1 z 1z 1 )(1 z 2 z 1 ) (1 p 1 z 1 )(1 p 2 z 1 ) (1) where z 1 and z 2 are the zeros, and p 1 and p 2 are the poles from part (b). (Remember that Matlab can multiply polynomials via its conv function.) Record the filter coefficients for later use. (d) Change the angle of the pole: move the pole to 90, then 135. Describe the changes in h[n] and H(e j ˆω ). (e) Increase the magnitude of the pole: first try 0.9, then 0.95, and then go outside the unit circle. Describe the changes in h[n] and H(e j ˆω ). 2
3 2 (a) FIR Filter 6 (b) Feedback Filter magnitude magnitude omega/pi omega/pi Figure 1: Magnitude response of two unknown filters. Use pez to help you find the filter coefficients that will match these frequency responses as closely as possible. (a) Second-order FIR filter. (b) Second-order IIR filter. 6 Filter Design In this section, we will use pez to place the poles and zeros to make a filter with a desirable frequency response. First of all, we will put poles at the origin and zeros on the unit circle to gain some understanding of these special cases. (a) Clear all the poles and zeros from pez. Now place a single pole at z = 0 and observe the impulse and frequency response. Now place another pole at the origin and observe carefully the changes in h[n] and the magnitude and phase of H(e j ˆω ). Finally, place a third pole at z = 0. What can you conclude about the effect of poles at the origin on the impulse response, magnitude response and phase response of a system? (b) Clear all poles and zeros from pez. Now place zeros at the following locations: z 1 = 1, z 2 =0 jand z 3 =0+j(remember that conjugate pairs such as z 2 and z 3 will be entered simultaneously). Judging from the impulse and frequency responses what type of filter have you just implemented? Measure (as best you can) the slope of the phase response. Design of a filter involves selecting the coefficients {a k } and {b k } to accomplish a given task. The task here is to create a filter that has a very narrow notch. This filter would be useful for removing one frequency component while leaving others undisturbed. The notch filter can be synthesized from the cascade of two simpler filters shown in Fig. 1. (c) Start the process by using pez to design each of the filters given in Fig. 1. Both filters are second-order. Make sure that you enter the poles and zeros precisely. pez will do the conversion between between root locations and polynomial coefficients, but you could also do this with the Matlab commands roots and poly. You should check your results by also calculating the filter coefficients by hand. Record the coefficients of your filters in the table provided. (d) Use freqz() to verify that the frequency response of each filter is correct. 3
4 (e) Now use pez to put the filters together in a cascade. Place the poles and zeros, and then view the frequency response. What are the filter coefficients for the cascaded filter H(z)? (f) Use freqz() to determine the frequency response of the cascade of the two filters that you designed in part (e). Plot the magnitude of the overall frequency response of the cascade system for 1 2 < ˆω/(2π) < 1 2, and print a copy of the plot for your lab report. Explain briefly why the frequency response magnitude has a notch, and explain why the gain at ˆω = 0 and ˆω = π is the same. 4
5 Worksheet for Observations Name: Date: Implemented 3-pt averager with pez: Part Observations 4(a) h[n] decays exponentially with no oscillations, H(e j ˆω ) has a hump at ˆω =0 4(b) 4(c) 4(d) 4(e) 4(f) 5(a) 5(b) 5(c) 5(d) 6(a) 6(b) Part 6(c,d,e,f) a k b k Filter 1 Filter 2 Cascade of 1 and 2 Explanation of cascade frequency response: 5
Signal Processing First Lab 11: PeZ - The z, n, and ˆω Domains
Signal Processing First Lab : PeZ - The z, n, and ˆω Domains The lab report/verification will be done by filling in the last page of this handout which addresses a list of observations to be made when
More information1 Introduction & Objective. 2 Warm-up. Lab P-16: PeZ - The z, n, and O! Domains
DSP First, 2e Signal Processing First Lab P-6: PeZ - The z, n, and O! Domains The lab report/verification will be done by filling in the last page of this handout which addresses a list of observations
More informationDSP First Lab 11: PeZ - The z, n, and ωdomains
DSP First Lab : PeZ - The, n, and ωdomains The lab report/verification will be done by filling in the last page of this handout which addresses a list of observations to be made when using the PeZ GUI.
More informationLecture 19 IIR Filters
Lecture 19 IIR Filters Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/5/10 1 General IIR Difference Equation IIR system: infinite-impulse response system The most general class
More informationLAB 2 - ONE DIMENSIONAL MOTION
Name Date Partners L02-1 LAB 2 - ONE DIMENSIONAL MOTION OBJECTIVES Slow and steady wins the race. Aesop s fable: The Hare and the Tortoise To learn how to use a motion detector and gain more familiarity
More informationLecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013
Today s Objectives ENGR 105: Feedback Control Design Winter 2013 Lecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013 1. introduce the MATLAB Control System Toolbox
More informationComputer Exercise 0 Simulation of ARMA-processes
Lund University Time Series Analysis Mathematical Statistics Fall 2018 Centre for Mathematical Sciences Computer Exercise 0 Simulation of ARMA-processes The purpose of this computer exercise is to illustrate
More informationPHY 111L Activity 2 Introduction to Kinematics
PHY 111L Activity 2 Introduction to Kinematics Name: Section: ID #: Date: Lab Partners: TA initials: Objectives 1. Introduce the relationship between position, velocity, and acceleration 2. Investigate
More informationLab 1 Uniform Motion - Graphing and Analyzing Motion
Lab 1 Uniform Motion - Graphing and Analyzing Motion Objectives: < To observe the distance-time relation for motion at constant velocity. < To make a straight line fit to the distance-time data. < To interpret
More informationCh. 7: Z-transform Reading
c J. Fessler, June 9, 3, 6:3 (student version) 7. Ch. 7: Z-transform Definition Properties linearity / superposition time shift convolution: y[n] =h[n] x[n] Y (z) =H(z) X(z) Inverse z-transform by coefficient
More information18-Dec-12 PHYS Simple Pendulum. To investigate the fundamental physical properties of a simple pendulum.
Objective Simple Pendulum To investigate the fundamental physical properties of a simple pendulum. Equipment Needed Simple Pendulum Apparatus with Meter Scale and Protractor Bobs 4 (Aluminum, Brass, Lead,
More informationForce vs time. IMPULSE AND MOMENTUM Pre Lab Exercise: Turn in with your lab report
IMPULSE AND MOMENTUM Pre Lab Exercise: Turn in with your lab report Newton s second law may be written r r F dt = p where F is the force and p is the change in momentum. The area under the force vs. time
More informationName Student ID # Instructor Lab Period Date Due. Lab 5 Continuity
Name Student ID # Instructor Lab Period Date Due Lab 5 Continuity Objectives 1. To visually represent the concept of continuity. 2. To develop an informal intuition for continuity. Continuity A fuction
More informationLab 15 Taylor Polynomials
Name Student ID # Instructor Lab Period Date Due Lab 15 Taylor Polynomials Objectives 1. To develop an understanding for error bound, error term, and interval of convergence. 2. To visualize the convergence
More informationES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK
ES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK What is SIMULINK? SIMULINK is a software package for modeling, simulating, and analyzing
More informationPhysics Spring 2006 Experiment 4. Centripetal Force. For a mass M in uniform circular motion with tangential speed v at radius R, the required
Centripetal Force I. Introduction. In this experiment you will study the centripetal force required for a mass in uniform circular motion. You will determine the centripetal forces required for different
More informationComputer simulation of radioactive decay
Computer simulation of radioactive decay y now you should have worked your way through the introduction to Maple, as well as the introduction to data analysis using Excel Now we will explore radioactive
More informationE : Lecture 1 Introduction
E85.2607: Lecture 1 Introduction 1 Administrivia 2 DSP review 3 Fun with Matlab E85.2607: Lecture 1 Introduction 2010-01-21 1 / 24 Course overview Advanced Digital Signal Theory Design, analysis, and implementation
More informationLab 1: Dynamic Simulation Using Simulink and Matlab
Lab 1: Dynamic Simulation Using Simulink and Matlab Objectives In this lab you will learn how to use a program called Simulink to simulate dynamic systems. Simulink runs under Matlab and uses block diagrams
More informationExperiment 13 Poles and zeros in the z plane: IIR systems
Experiment 13 Poles and zeros in the z plane: IIR systems Achievements in this experiment You will be able to interpret the poles and zeros of the transfer function of discrete-time filters to visualize
More informationBCMB/CHEM 8190 Lab Exercise Using Maple for NMR Data Processing and Pulse Sequence Design March 2012
BCMB/CHEM 8190 Lab Exercise Using Maple for NMR Data Processing and Pulse Sequence Design March 2012 Introduction Maple is a powerful collection of routines to aid in the solution of mathematical problems
More information5-Sep-15 PHYS101-2 GRAPHING
GRAPHING Objectives 1- To plot and analyze a graph manually and using Microsoft Excel. 2- To find constants from a nonlinear relation. Exercise 1 - Using Excel to plot a graph Suppose you have measured
More informationLaboratory handouts, ME 340
Laboratory handouts, ME 340 This document contains summary theory, solved exercises, prelab assignments, lab instructions, and report assignments for Lab 4. 2014-2016 Harry Dankowicz, unless otherwise
More information3 Charged Particle Motion in a Magnetic Field
3 Charged Particle Motion in a Magnetic Field When you have completed the Particle Annihilation section and read all the text (especially section 2.2), click the Next button in the Particle Annihilation
More informationTALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 6. THE TEMPERATURE DEPENDANCE OF RESISTANCE
6. THE TEMPERATURE DEPENDANCE OF RESISTANCE 1. Objective Determining temperature coefficient of metal and activation energy of self-conductance of semiconductor sample. 2. Equipment needed Metal and semiconductor
More informationKinematics Lab. 1 Introduction. 2 Equipment. 3 Procedures
Kinematics Lab 1 Introduction An object moving in one dimension and undergoing constant or uniform acceleration has a position given by: x(t) =x 0 +v o t +1/2at 2 where x o is its initial position (its
More informationSignificant Figures and an Introduction to the Normal Distribution
Significant Figures and an Introduction to the Normal Distribution Object: To become familiar with the proper use of significant figures and to become acquainted with some rudiments of the theory of measurement.
More informationME scope Application Note 28
App Note 8 www.vibetech.com 3/7/17 ME scope Application Note 8 Mathematics of a Mass-Spring-Damper System INTRODUCTION In this note, the capabilities of ME scope will be used to build a model of the mass-spring-damper
More informationMATLAB BASICS. Instructor: Prof. Shahrouk Ahmadi. TA: Kartik Bulusu
MATLAB BASICS Instructor: Prof. Shahrouk Ahmadi 1. What are M-files TA: Kartik Bulusu M-files are files that contain a collection of MATLAB commands or are used to define new MATLAB functions. For the
More informationEXPERIMENT 4 ONE DIMENSIONAL MOTION
EXPERIMENT 4 ONE DIMENSIONAL MOTION INTRODUCTION This experiment explores the meaning of displacement; velocity, acceleration and the relationship that exist between them. An understanding of these concepts
More informationMultivariable Control Laboratory experiment 2 The Quadruple Tank 1
Multivariable Control Laboratory experiment 2 The Quadruple Tank 1 Department of Automatic Control Lund Institute of Technology 1. Introduction The aim of this laboratory exercise is to study some different
More informationConservation of Mechanical Energy Activity Purpose
Conservation of Mechanical Energy Activity Purpose During the lab, students will become familiar with solving a problem involving the conservation of potential and kinetic energy. A cart is attached to
More informationIntroduction to Hartree-Fock calculations in Spartan
EE5 in 2008 Hannes Jónsson Introduction to Hartree-Fock calculations in Spartan In this exercise, you will get to use state of the art software for carrying out calculations of wavefunctions for molecues,
More informationJaguar DFT Optimizations and Transition State Searches
Jaguar DFT Optimizations and Transition State Searches Density Functional Theory (DFT) is a quantum mechanical (QM) method that gives results superior to Hartree Fock (HF) in less computational time. A
More informationLab 1: Earthquake Resources & Plotting Epicenters
Name Geophysics of Earthquakes Lab 1: Earthquake Resources & Plotting Epicenters Your Mission: (1) Learn how to use an Internet earthquake database to access important information about earthquakes from
More informationDriven Harmonic Oscillator
Driven Harmonic Oscillator Physics 6B Lab Experiment 1 APPARATUS Computer and interface Mechanical vibrator and spring holder Stands, etc. to hold vibrator Motion sensor C-209 spring Weight holder and
More informationDamped Oscillators (revisited)
Damped Oscillators (revisited) We saw that damped oscillators can be modeled using a recursive filter with two coefficients and no feedforward components: Y(k) = - a(1)*y(k-1) - a(2)*y(k-2) We derived
More informationExperiment P05: Position, Velocity, & Acceleration (Motion Sensor)
PASCO scientific Physics Lab Manual: P05-1 Experiment P05: Position, Velocity, & Acceleration (Motion Sensor) Concept Time SW Interface Macintosh file Windows file linear motion 30 m 500 or 700 P05 Position,
More informationUniversity of TN Chattanooga Physics 1040L 8/18/2012 PHYSICS 1040L LAB LAB 4: R.C. TIME CONSTANT LAB
PHYSICS 1040L LAB LAB 4: R.C. TIME CONSTANT LAB OBJECT: To study the discharging of a capacitor and determine the time constant for a simple circuit. APPARATUS: Capacitor (about 24 μf), two resistors (about
More informationProject IV Fourier Series
Project IV Fourier Series Robert Jerrard Goal of the project To develop understanding of how many terms of a Fourier series are required in order to well-approximate the original function, and of the differences
More informationECE 220 Laboratory 4 Volt Meter, Comparators, and Timer
ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory
More informationLaboratory 11 Control Systems Laboratory ECE3557. State Feedback Controller for Position Control of a Flexible Joint
Laboratory 11 State Feedback Controller for Position Control of a Flexible Joint 11.1 Objective The objective of this laboratory is to design a full state feedback controller for endpoint position control
More informationConservation of Mechanical Energy Activity Purpose
Conservation of Mechanical Energy Activity Purpose During the lab, students will become familiar with solving a problem involving the conservation of potential and kinetic energy. A cart is attached to
More informationLecture 3 Matlab Simulink Minimum Phase, Maximum Phase and Linear Phase Systems
Lecture 3 Matlab Simulink Minimum Phase, Maximum Phase and Linear Phase Systems Lester Liu October 31, 2012 Minimum Phase, Maximum Phase and Linear Phase LTI Systems In this section, we will explore the
More informationZ - Transform. It offers the techniques for digital filter design and frequency analysis of digital signals.
Z - Transform The z-transform is a very important tool in describing and analyzing digital systems. It offers the techniques for digital filter design and frequency analysis of digital signals. Definition
More informationSpectrometer User s Guide
Spectrometer User s Guide (Order Codes: V-SPEC, SPRT-VIS, SP-VIS, SP-UV-VIS, ESRT-VIS) The spectrometer is a portable light spectrophotometer, combining a spectrometer and a light source/cuvette holder.
More information2: SIMPLE HARMONIC MOTION
2: SIMPLE HARMONIC MOTION Motion of a mass hanging from a spring If you hang a mass from a spring, stretch it slightly, and let go, the mass will go up and down over and over again. That is, you will get
More informationCenter of Mass. Evaluation copy
Center of Mass Experiment 19 INTRODUCTION In the most of the previous experiments you have examined the motion of a single object as it underwent a variety of motions. You learned that an object subject
More informationCentre for Mathematical Sciences HT 2017 Mathematical Statistics. Study chapters 6.1, 6.2 and in the course book.
Lund University Stationary stochastic processes Centre for Mathematical Sciences HT 2017 Mathematical Statistics Computer exercise 2 in Stationary stochastic processes, HT 17. The purpose with this computer
More informationApplications of Newton's Laws
Applications of Newton's Laws Purpose: To apply Newton's Laws by applying forces to objects and observing their motion; directly measuring these forces that are applied. Apparatus: Pasco track, Pasco cart,
More informationRate Law Determination of the Crystal Violet Reaction. Evaluation copy
Rate Law Determination of the Crystal Violet Reaction Computer 30 In this experiment, you will observe the reaction between crystal violet and sodium hydroxide. One objective is to study the relationship
More informationTutorial 23 Back Analysis of Material Properties
Tutorial 23 Back Analysis of Material Properties slope with known failure surface sensitivity analysis probabilistic analysis back analysis of material strength Introduction Model This tutorial will demonstrate
More informationCHARTING THE HEAVENS USING A VIRTUAL PLANETARIUM
Name Partner(s) Section Date CHARTING THE HEAVENS USING A VIRTUAL PLANETARIUM You have had the opportunity to look at two different tools to display the night sky, the celestial sphere and the star chart.
More informationPurpose: Materials: WARNING! Section: Partner 2: Partner 1:
Partner 1: Partner 2: Section: PLEASE NOTE: You will need this particular lab report later in the semester again for the homework of the Rolling Motion Experiment. When you get back this graded report,
More informationKinetics of Crystal Violet Bleaching
Kinetics of Crystal Violet Bleaching Authors: V. C. Dew and J. M. McCormick* From Update March 12, 2013 with revisions Nov. 29, 2016 Introduction Chemists are always interested in whether a chemical reaction
More informationUsing Microsoft Excel
Using Microsoft Excel Objective: Students will gain familiarity with using Excel to record data, display data properly, use built-in formulae to do calculations, and plot and fit data with linear functions.
More informationLecture 7 Discrete Systems
Lecture 7 Discrete Systems EE 52: Instrumentation and Measurements Lecture Notes Update on November, 29 Aly El-Osery, Electrical Engineering Dept., New Mexico Tech 7. Contents The z-transform 2 Linear
More informationState Feedback Controller for Position Control of a Flexible Link
Laboratory 12 Control Systems Laboratory ECE3557 Laboratory 12 State Feedback Controller for Position Control of a Flexible Link 12.1 Objective The objective of this laboratory is to design a full state
More informationPhotoelectric Photometry of the Pleiades Student Manual
Name: Lab Partner: Photoelectric Photometry of the Pleiades Student Manual A Manual to Accompany Software for the Introductory Astronomy Lab Exercise Edited by Lucy Kulbago, John Carroll University 11/24/2008
More informationLecture 2 OKAN UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE
OKAN UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE EEE 43 DIGITAL SIGNAL PROCESSING (DSP) 2 DIFFERENCE EQUATIONS AND THE Z- TRANSFORM FALL 22 Yrd. Doç. Dr. Didem Kivanc Tureli didemk@ieee.org didem.kivanc@okan.edu.tr
More information2 Background: Fourier Series Analysis and Synthesis
Signal Processing First Lab 15: Fourier Series Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up sections of this lab assignment and go over all exercises in the Pre-Lab section before
More informationDetermination of Density 1
Introduction Determination of Density 1 Authors: B. D. Lamp, D. L. McCurdy, V. M. Pultz and J. M. McCormick* Last Update: February 1, 2013 Not so long ago a statistical data analysis of any data set larger
More informationPHY 123 Lab 4 - Conservation of Energy
1 PHY 123 Lab 4 - Conservation of Energy The purpose of this lab is to verify the conservation of mechanical energy experimentally. Important! You need to print out the 1 page worksheet you find by clicking
More informationAugust 7, 2007 NUMERICAL SOLUTION OF LAPLACE'S EQUATION
August 7, 007 NUMERICAL SOLUTION OF LAPLACE'S EQUATION PURPOSE: This experiment illustrates the numerical solution of Laplace's Equation using a relaxation method. The results of the relaxation method
More informationCHARTING THE HEAVENS USING A VIRTUAL PLANETARIUM
Name Partner(s) Section Date CHARTING THE HEAVENS USING A VIRTUAL PLANETARIUM You have had the opportunity to look at two different tools to display the night sky, the celestial sphere and the star chart.
More informationAppendix 3B MATLAB Functions for Modeling and Time-domain analysis
Appendix 3B MATLAB Functions for Modeling and Time-domain analysis MATLAB control system Toolbox contain the following functions for the time-domain response step impulse initial lsim gensig damp ltiview
More informationHarvard Life Science Outreach December 7, 2017 Measuring ecosystem carbon fluxes using eddy covariance data ACTIVITIES I. NAME THAT ECOSYSTEM!
Harvard Life Science Outreach December 7, 2017 Measuring ecosystem carbon fluxes using eddy covariance data ACTIVITIES I. NAME THAT ECOSYSTEM! Objective: Distinguish ecosystems (tropical forest vs. temperate
More informationCalculating Bond Enthalpies of the Hydrides
Proposed Exercise for the General Chemistry Section of the Teaching with Cache Workbook: Calculating Bond Enthalpies of the Hydrides Contributed by James Foresman, Rachel Fogle, and Jeremy Beck, York College
More informationExperiment 0: Periodic Signals and the Fourier Series
University of Rhode Island Department of Electrical and Computer Engineering ELE : Communication Systems Experiment : Periodic Signals and the Fourier Series Introduction In this experiment, we will investigate
More informationDetermining the Conductivity of Standard Solutions
Determining the Conductivity of Standard Solutions by Anna Cole and Shannon Clement Louisiana Curriculum Framework Content Strand: Science as Inquiry, Physical Science Grade Level 11-12 Objectives: 1.
More informationCart on a Ramp. Evaluation Copy. Figure 1. Vernier Dynamics Track. Motion Detector Bracket
Cart on a Ramp Computer 3 This experiment uses an incline and a low-friction cart. If you give the cart a gentle push up the incline, the cart will roll upward, slow and stop, and then roll back down,
More informationHow many states. Record high temperature
Record high temperature How many states Class Midpoint Label 94.5 99.5 94.5-99.5 0 97 99.5 104.5 99.5-104.5 2 102 102 104.5 109.5 104.5-109.5 8 107 107 109.5 114.5 109.5-114.5 18 112 112 114.5 119.5 114.5-119.5
More informationMeasuring the time constant for an RC-Circuit
Physics 8.02T 1 Fall 2001 Measuring the time constant for an RC-Circuit Introduction: Capacitors Capacitors are circuit elements that store electric charge Q according to Q = CV where V is the voltage
More informationBUILDING BASICS WITH HYPERCHEM LITE
BUILDING BASICS WITH HYPERCHEM LITE LAB MOD1.COMP From Gannon University SIM INTRODUCTION A chemical bond is a link between atoms resulting from the mutual attraction of their nuclei for electrons. There
More informationOECD QSAR Toolbox v.4.1. Tutorial illustrating new options for grouping with metabolism
OECD QSAR Toolbox v.4.1 Tutorial illustrating new options for grouping with metabolism Outlook Background Objectives Specific Aims The exercise Workflow 2 Background Grouping with metabolism is a procedure
More informationOCEAN/ESS 410 Lab 4. Earthquake location
Lab 4. Earthquake location To complete this exercise you will need to (a) Complete the table on page 2. (b) Identify phases on the seismograms on pages 3-6 as requested on page 11. (c) Locate the earthquake
More informationPolar alignment in 5 steps based on the Sánchez Valente method
1 Polar alignment in 5 steps based on the Sánchez Valente method Compared to the drift alignment method, this one, allows you to easily achieve a perfect polar alignment in just one step. By "perfect polar
More informationz-transforms Definition of the z-transform Chapter
z-transforms Chapter 7 In the study of discrete-time signal and systems, we have thus far considered the time-domain and the frequency domain. The z- domain gives us a third representation. All three domains
More informationLinear Motion with Constant Acceleration
Linear Motion 1 Linear Motion with Constant Acceleration Overview: First you will attempt to walk backward with a constant acceleration, monitoring your motion with the ultrasonic motion detector. Then
More informationNewton s Second Law. Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m.
Newton s Second Law Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m. F net = ma (1) It should come as no surprise that this force produces an
More informationa. Follow the Start-Up Procedure in the laboratory manual. Note the safety rules.
Lab #1 - Free Vibration Name: Date: Section / Group: Procedure Steps (from lab manual): a. Follow the Start-Up Procedure in the laboratory manual. Note the safety rules. b. Locate the various springs and
More informationBasic chromatographic parameters and optimization in LC
AM0925 Assignment Basic chromatographic parameters and optimization in LC Introduction This is a computer exercise where you will apply a simulator of reversed phase LC to study the influence of chromatographic
More informationLab 10 Logarithmic Functions
Name Student ID # Instructor Lab Period Date Due Lab 10 Logarithmic Functions Objectives 1. To develop an ability to visualize the graphs of logarithmic functions. 2. To become familiar with applications
More informationDiscrete Time Systems
Discrete Time Systems Valentina Hubeika, Jan Černocký DCGM FIT BUT Brno, {ihubeika,cernocky}@fit.vutbr.cz 1 LTI systems In this course, we work only with linear and time-invariant systems. We talked about
More informationRadiation. Laboratory exercise - Astrophysical Radiation Processes. Magnus Gålfalk Stockholm Observatory 2007
Radiation Laboratory exercise - Astrophysical Radiation Processes Magnus Gålfalk Stockholm Observatory 2007 1 1 Introduction The electric (and magnetic) field pattern from a single charged particle can
More informationCHM201 General Chemistry and Laboratory I Laboratory 7 Thermochemistry and Hess s Law May 2, 2018
Purpose: CHM201 General Chemistry and Laboratory I Laboratory 7 Thermochemistry and Hess s Law May 2, 2018 In this laboratory, you will measure heat changes arising from chemical reactions. You will use
More informationHow to Make or Plot a Graph or Chart in Excel
This is a complete video tutorial on How to Make or Plot a Graph or Chart in Excel. To make complex chart like Gantt Chart, you have know the basic principles of making a chart. Though I have used Excel
More informationPS403 - Digital Signal processing
PS403 - Digital Signal processing 6. DSP - Recursive (IIR) Digital Filters Key Text: Digital Signal Processing with Computer Applications (2 nd Ed.) Paul A Lynn and Wolfgang Fuerst, (Publisher: John Wiley
More informationSpace Group & Structure Solution
Space Group & Structure Solution Determine the Space Group Space group determination can always be performed by hand by examining the intensity data. A program that can facilitate this step is the command-prompt
More informationCoefficient of Friction Lab
Name Date Period Coefficient of Friction Lab The purpose of this lab is to determine the relationship between a) the force of static friction and the normal force and b) the force of kinetic friction and
More informationPhotoelectric Photometry of the Pleiades
Photoelectric Photometry of the Pleiades Student Manual A Manual to Accompany Software for the Introductory Astronomy Lab Exercise Document SM 2: Version 0.96lab Department of Physics Gettysburg College
More informationPHYSICS LAB Experiment 7 Fall 2004 CONSERVATION OF MOMENTUM & COLLISIONS
PHYSICS 83 - LAB Experiment 7 Fall 004 CONSERVATION OF MOMENTUM & COLLISIONS In this experiment we will study how the total vector momentum of an isolated system is conserved (remains constant) in collisions.
More informationFree Fall. v gt (Eq. 4) Goals and Introduction
Free Fall Goals and Introduction When an object is subjected to only a gravitational force, the object is said to be in free fall. This is a special case of a constant-acceleration motion, and one that
More informationPartner s Name: EXPERIMENT MOTION PLOTS & FREE FALL ACCELERATION
Name: Partner s Name: EXPERIMENT 500-2 MOTION PLOTS & FREE FALL ACCELERATION APPARATUS Track and cart, pole and crossbar, large ball, motion detector, LabPro interface. Software: Logger Pro 3.4 INTRODUCTION
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Experiment 03: Work and Energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Fall Term 2010 Experiment 03: Work and Energy Purpose of the Experiment: In this experiment you allow a cart to roll down an inclined
More informationLife Cycle of Stars. Photometry of star clusters with SalsaJ. Authors: Daniel Duggan & Sarah Roberts
Photometry of star clusters with SalsaJ Authors: Daniel Duggan & Sarah Roberts Photometry of star clusters with SalsaJ Introduction Photometry is the measurement of the intensity or brightness of an astronomical
More informationECE4270 Fundamentals of DSP Lecture 20. Fixed-Point Arithmetic in FIR and IIR Filters (part I) Overview of Lecture. Overflow. FIR Digital Filter
ECE4270 Fundamentals of DSP Lecture 20 Fixed-Point Arithmetic in FIR and IIR Filters (part I) School of ECE Center for Signal and Information Processing Georgia Institute of Technology Overview of Lecture
More informationPhotoelectric Photometry of the Pleiades
Photoelectric Photometry of the Pleiades Student Manual A Manual to Accompany Software for the Introductory Astronomy Lab Exercise Document SM 2: Version 1 Department of Physics Gettysburg College Gettysburg,
More informationEE102B Signal Processing and Linear Systems II. Solutions to Problem Set Nine Spring Quarter
EE02B Signal Processing and Linear Systems II Solutions to Problem Set Nine 202-203 Spring Quarter Problem 9. (25 points) (a) 0.5( + 4z + 6z 2 + 4z 3 + z 4 ) + 0.2z 0.4z 2 + 0.8z 3 x[n] 0.5 y[n] -0.2 Z
More informationPHY221 Lab 2 - Experiencing Acceleration: Motion with constant acceleration; Logger Pro fits to displacement-time graphs
Page 1 PHY221 Lab 2 - Experiencing Acceleration: Motion with constant acceleration; Logger Pro fits to displacement-time graphs Print Your Name Print Your Partners' Names You will return this handout to
More information