Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of...

13
Numerical Operation s S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan- Dearborn Introduction to Matlab: Numerical Interpolation

Transcript of Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of...

Page 1: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

Numerical Operations

S. Awad, Ph.D.

M. Corless, M.S.E.E.

E.C.E. Department

University of Michigan-Dearborn

Introduction to Matlab:

Numerical Interpolation

Page 2: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

2

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Interpolation Topics

1D Interpolation Interp1 Command Spline Command 2D Interpolation Interp2 Command

Page 3: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

3

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

1-D Interpolation

Given xdata and ydata

Want to estimate the values of the function: xi=[xi(1) xi(2) … ]’ % values of x

The command interp1 is used for One Dimensional Interpolation

Page 4: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

4

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

interp1 Command

yi=interp1(xdata,ydata,xi,method)

Where the method of interpolation can be:

‘linear’ for linear interpolation ‘spline’ for Spline Interpolation ‘cubic’ for Cubic Interpolation

Page 5: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

5

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

A Coarse Sine Wave

» xdata=[0:pi/4:2*pi]';

» ydata=sin(xdata);

» plot(xdata,ydata);

» title('Course

Sine Wave');

» xlabel('xdata');

» ylabel('ydata');

Page 6: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

6

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Interpolated Sine Wave

» xi=[0:pi/64:2*pi]';

» yi=interp1(xdata,

ydata,xi,'spline');

» plot(xi,yi)

» title('Interpolated

Sine Wave');

» xlabel('xi');

» ylabel('yi');

Page 7: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

7

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Good Fit & Error Check for Good Fit

» plot(xi,sin(xi),'r',xi,yi,'x');

Check For Error

» plot(xi,(yi-sin(xi)));

Page 8: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

8

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Spline Use spline for a cubic spline interpolation method

» yi=spline(xdata,ydata,xi);

» plot(xi,yi);

» title('Cubic Spline

Interpolation');

» xlabel('xi');

» ylabel('yi');

Page 9: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

9

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

2-D Interpolation Consider the following sheet of metal with the

following temperatures at different points:

1 2 3 4 5 x1 82° 81° 80° 82° 84°2 79° 63° 61° 65° 81°3 84° 84° 82° 85° 86°

y

We will estimate the temperatures on a finer scale

Page 10: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

10

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Plot Original Mesh Set up Matrices in Matlab

» z=[82 81 80 82 84

79 63 61 65 81

84 84 82 85 86];

» xdata =[1:5];

» ydata=[1:3]';

Plot the Original Mesh

» mesh(xdata,ydata,z);

» title('Original Metal Temps');

» zlabel('temp');

Page 11: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

11

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Original Mesh

Course Concave

Page 12: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

12

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

Finer 2-D Interpolation Estimate Temperature Surface to a finer scale using the interp2 command

» xi=[1:0.1:5];

» yi=[1:0.2:3]';

» zi=interp2(xdata,ydata,z,xi,yi,'cubic');

% or ‘linear’ or ‘spline’

» mesh(xi,yi,zi);

» title('2D Interp Metal Temps');

» zlabel('temp');

Page 13: Numerical Operations S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Introduction to Matlab: Numerical Interpolation.

13

Numerical Operations:U of M-Dearborn ECE DepartmentIntroduction to MATLAB and its Toolboxes

Interpolation

2-D Interpolated Mesh

Smooth Concave


LECTURE ON MOBILE COMMUNICATION SYSTEMS BY Mukul Mittal Lecturer E.C.E G.P.C.G, Patiala(9463376309) mukul_mittal85@yahoo.co.in.

LECTURE ON MOBILE COMMUNICATION SYSTEMS BY Mukul Mittal Lecturer E.C.E G.P.C.G, Patiala(9463376309) [email protected].

SR Theory of Electrodynamics for Relative Moving Charges By James Keele, M.S.E.E. October 27, 2012.

SR Theory of Electrodynamics for Relative Moving Charges By James Keele, M.S.E.E. October 27, 2012.

S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Differential Equations Math Review with Matlab: First Order Constant.

S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Differential Equations Math Review with Matlab: First Order Constant.

8 INTERNATIONAL CONFERENCE on RENEWABLE ENERGY · Biography: Professor Atsuo Kawamura received the B.S.E.E., M.S.E.E., and Ph.D. degrees in electrical engineering from the University

8 INTERNATIONAL CONFERENCE on RENEWABLE ENERGY · Biography: Professor Atsuo Kawamura received the B.S.E.E., M.S.E.E., and Ph.D. degrees in electrical engineering from the University

Solving Algebraic Equations S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn Math Review with Matlab:

Solving Algebraic Equations S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn Math Review with Matlab:

1 Name of the faculty: V. Narsimha Reddy Designation: Lecturer in EEE Branch : E.C.E. Institute : GMR. Polytechnic Gajwel Year / Semester : VI Semester.

1 Name of the faculty: V. Narsimha Reddy Designation: Lecturer in EEE Branch : E.C.E. Institute : GMR. Polytechnic Gajwel Year / Semester : VI Semester.

E.C.E Seminar Topics

E.C.E Seminar Topics

Fourier Analysis S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn Math Review with Matlab: Fourier Series.

Fourier Analysis S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn Math Review with Matlab: Fourier Series.

EFFICIENT AND ENHANCED CARRY SELECT ADDER · PDF fileEFFICIENT AND ENHANCED CARRY SELECT ADDER FOR MULTIPURPOSE APPLICATIONS A.RAMESH Asst. Professor, E.C.E

EFFICIENT AND ENHANCED CARRY SELECT ADDER · PDF fileEFFICIENT AND ENHANCED CARRY SELECT ADDER FOR MULTIPURPOSE APPLICATIONS A.RAMESH Asst. Professor, E.C.E

Numerical Differentiation & Integration Numerical Differentiation I · 2012. 2. 27. · Numerical Differentiation & Integration Numerical Differentiation I Numerical Analysis (9th

Numerical Differentiation & Integration Numerical Differentiation I · 2012. 2. 27. · Numerical Differentiation & Integration Numerical Differentiation I Numerical Analysis (9th

Numerical Numerical Methods Carnahan

Numerical Numerical Methods Carnahan

Time state Athanassios Katsamanis, George Papandreou, Petros Maragos School of E.C.E., National Technical University of Athens, Athens 15773, Greece Audiovisual-to-articulatory.

Time state Athanassios Katsamanis, George Papandreou, Petros Maragos School of E.C.E., National Technical University of Athens, Athens 15773, Greece Audiovisual-to-articulatory.

ADVANCED STATIC CONTROL Mitigating Electrostatic Effects on Measurement Accuracy Arnold Steinman M.S.E.E. Electrostatics Consultant Electronics Workshop.

ADVANCED STATIC CONTROL Mitigating Electrostatic Effects on Measurement Accuracy Arnold Steinman M.S.E.E. Electrostatics Consultant Electronics Workshop.

Overview of Autonomous Vehicle Sensors and …iieom.org/ICMOE2015/papers/140.pdfOverview of Autonomous Vehicle Sensors and Systems Jaycil Z. Varghese M.S.E.E. Candidate University

Overview of Autonomous Vehicle Sensors and …iieom.org/ICMOE2015/papers/140.pdfOverview of Autonomous Vehicle Sensors and Systems Jaycil Z. Varghese M.S.E.E. Candidate University

Fourier Analysis Math Review with Matlab: Fourier Transform S. Awad, Ph.D. D. Cinpinski E.C.E. Department University of Michigan-Dearborn.

Fourier Analysis Math Review with Matlab: Fourier Transform S. Awad, Ph.D. D. Cinpinski E.C.E. Department University of Michigan-Dearborn.

Information Theoretic Sensor Managementssg.mit.edu/.../Williams_PhD_2_07.pdf · Jason L. Williams B.E.(Electronics)(Hons.) B.Inf.Tech., Queensland University of Technology, 1999 M.S.E.E.,

Information Theoretic Sensor Managementssg.mit.edu/.../Williams_PhD_2_07.pdf · Jason L. Williams B.E.(Electronics)(Hons.) B.Inf.Tech., Queensland University of Technology, 1999 M.S.E.E.,

DIRECT NUMERICAL SIMULATION DIRECT NUMERICAL ...direct numerical simulation direct

DIRECT NUMERICAL SIMULATION DIRECT NUMERICAL ...direct numerical simulation direct

CPSC 603 Database Systems Lecturer: Laurie Webster II, M.S.S.E., M.S.E.E., M.S.BME, Ph.D., P.E. Lecture 3 Introduction to a First Course in Database Systems.

CPSC 603 Database Systems Lecturer: Laurie Webster II, M.S.S.E., M.S.E.E., M.S.BME, Ph.D., P.E. Lecture 3 Introduction to a First Course in Database Systems.

Continuing Education Program Construction Costs Estimating Prof. Jaime José Laracuente-Díaz, M.S.E.E., P.E. Instructor @ the Department of ElectronicsDepartment.

Continuing Education Program Construction Costs Estimating Prof. Jaime José Laracuente-Díaz, M.S.E.E., P.E. Instructor @ the Department of ElectronicsDepartment.

S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Laplace Transform Math Review with Matlab: Application: Linear Time.

S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn Laplace Transform Math Review with Matlab: Application: Linear Time.