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Matlab

Hira Sisodiya, profile picture
Hira Sisodiya

This document discusses using MATLAB to generate a sine wave with minimal computational complexity. It shows that a sine wave can be generated with just three lines of code by plotting x values from 0.1 to 10 against sine of x. This demonstrates MATLAB's simplicity and power as an engineering tool.

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1 C Language is Simplest.
2 What may be the size of the program for writing a C code that generates sin wave?
3 But we can do the same by only three lines.
x=0.1:0.1:10; 4 b=sin(x); Plot(x,b) ------ no computational complexity
5 That is the beauty we have as an engineer. Name is MATLAB
Recent Trends in Computational techniques for Engineering 6 Use of MATLAB in Engineering Prof. Ashish M. Kothari Department of Electronics & Communication Engineering Atmiya Institute of Technology & Science, Rajkot
Topics.. 7 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
Topics.. 8 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions
MATLAB 9 “MATrix LABoratory” Powerful, extensible, highly integrated computation, programming, visualization, and simulation package Widely used in engineering, mathematics, and science
MATLAB 10 Everything in MATLAB is a matrix !
MATLAB- Starting & Quiting 11 Starting MATLAB On a Microsoft Windows platform, to start MATLAB, double-click the MATLAB shortcut icon on your Windows desktop. On Linux, to start MATLAB, type matlab at the operating system prompt. After starting MATLAB, the MATLAB desktop opens – see “MATLAB Desktop”. You can change the directory in which MATLAB starts, define startup options including running a script upon startup, and reduce startup time in some situations.
MATLAB- Starting & Quiting 12 Quiting MATLAB To end your MATLAB session, select Exit MATLAB from the File menu in the desktop, or type quit in the Command Window.
The MATLAB Desktop 13
Matlab
MATLAB Variable 15 Variable names ARE case sensitive Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer) Variable names must start with a letter followed by letters, digits, and underscores.
MATLAB Variable 16 >> 16 + 24 no declarations needed ans = 40 >> product = 16 * 23.24 mixed data types product = 371.84 semi-colon suppresses output of >> product = 16 *555.24; the calculation’s result >> product product = 8883.8
MATLAB Variable 17 >> clear clear removes all variables; >> product = 2 * 3^3; >> comp_sum = (2 + 3i) + (2 - 3i); clear x y removes only x and y >> show_i = i^2; complex numbers (i or j) require >> save three_things no special handling >> clear >> load three_things >> who save/load are used to Your variables are: comp_sum product show_i retain/restore workspace variables >> product product = 54 use home to clear screen and put >> show_i cursor at the top of the screen show_i = -1
MATLAB Special Variables 18 ans Default variable name for results pi Value of π eps Smallest incremental number inf Infinity NaN Not a number e.g. 0/0 i and j i = j = square root of -1 realmin The smallest usable positive real number realmax The largest usable positive real number
Topics.. 19 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
Math & Assignment Operators 20 Power ^ or .^ e.g a^b or a.^b Multiplication * or .* e.g a*b or a.*b Division / or ./ e.g a/b or a./b or or . e.g ba or b.a NOTE: 56/8 = 856 - (unary) + (unary) Addition + a+b Subtraction - a-b Assignment = a=b (assign b to a)
Other MATLAB symbols 21 >> prompt ... continue statement on next line , separate statements and data % start comment which ends at end of line ; (1) suppress output (2) used as a row separator in a matrix : specify range
MATLAB Relational Operators 22 MATLAB supports six relational operators. Less Than < Less Than or Equal <= Greater Than > Greater Than or Equal >= Equal To == Not Equal To ~=
MATLAB Logical Operators 23 MATLAB supports three logical operators. not ~ % highest precedence and & % equal precedence with or or | % equal precedence with and
MATLAB Matrices 24 MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored. Vectors are special forms of matrices and contain only one row OR one column. Scalars are matrices with only one row AND one column
MATLAB Matrices 25 A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows: » a_value=23 a_value = 23
MATLAB Matrices 26 A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas): » rowvec = [12 , 14 , 63] rowvec = 12 14 63
MATLAB Matrices 27 A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons): » colvec = [13 ; 45 ; -2] colvec = 13 45 -2
MATLAB Matrices 28 A matrix can be created in MATLAB as follows (note the commas AND semicolons): » matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9] matrix = 1 2 3 4 5 6 7 8 9
Extracting a Sub-Matrix 29 A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices and the rows and columns to extract. The syntax is: sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ; where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix.
MATLAB Matrices 30 A column vector can be Here we extract column 2 extracted from a matrix. of the matrix and make a As an example we create a column vector: matrix below: » matrix=[1,2,3;4,5,6;7,8,9] » col_two=matrix( : , 2) matrix = col_two = 1 2 3 4 5 6 2 7 8 9 5 8
MATLAB Matrices 31 A row vector can be Here we extract row 2 of extracted from a matrix. the matrix and make a As an example we create row vector. Note that a matrix below: the 2:2 specifies the second row and the 1:3 » matrix=[1,2,3;4,5,6;7,8,9] specifies which columns of the row. matrix = » rowvec=matrix(2 : 2 , 1 : 3) 1 2 3 4 5 6 rowvec = 7 8 9 4 5 6
Topics.. 32 What is MATLAB ?? Basic Matrix Operations Script Files /M-files and Function Files Some more Operations and Functions Plotting functions ..
Use of M-File 33 There are two kinds of M-files: Scripts, which do not accept input arguments or return output arguments. They operate on data in the workspace. Functions, which can accept input arguments and return output arguments. Internal variables are local to the function. Click to create a new M-File
M-File as script file 34 Save file as filename.m Type what you want to do, eg. Create matrices If you include “;” at the end of each statement, result will not be shown immediately Run the file by typing the filename in the command window
MATLAB Function File 35 function [a b c] = myfun(x, y) Write these two lines to a file myfun.m b = x * y; a = 100; c = x.^2; and save it on MATLAB’s path >> myfun(2,3) % called with zero outputs ans = 100 >> u = myfun(2,3) % called with one output u = 100 >> [u v w] = myfun(2,3) % called with all outputs u = 100 v = Any return value which is not stored in 6 an output variable is simply discarded w = 4
Topics.. 36 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
Some Useful MATLAB commands 37 who List known variables whos List known variables plus their size help >> help sqrt Help on using sqrt lookfor >> lookfor sqrt Search for keyword sqrt in m-files what >> what a: List MATLAB files in a: clear Clear all variables from work space clear x y Clear variables x and y from work space clc Clear the command window
Some Useful MATLAB commands 38 what List all m-files in current directory dir List all files in current directory ls Same as dir type test Display test.m in command window delete test Delete test.m cd a: Change directory to a: chdir a: Same as cd pwd Show current directory which test Display directory path to ‘closest’ test.m
MATLAB Logical Functions 39 MATLAB also supports some logical functions. xor (exclusive or) Ex: xor (a, b) Where a and b are logical expressions. The xor operator evaluates to true if and only if one expression is true and the other is false. True is returned as 1, false as 0. any (x) returns 1 if any element of x is nonzero all (x) returns 1 if all elements of x are nonzero isnan (x) returns 1 at each NaN in x isinf (x) returns 1 at each infinity in x finite (x) returns 1 at each finite value in x
Matlab Selection Structures 40 An if - elseif - else structure in MATLAB. Note that elseif is one word. if expression1 % is true % execute these commands elseif expression2 % is true % execute these commands else % the default % execute these commands end
MATLAB Repetition Structures 41 A for loop in MATLAB for x = array for ind = 1:100 b(ind)=sin(ind/10) end while loop in MATLAB while expression while x <= 10 % execute these commands end
42 x=0.1:0.1:10; b=sin(x); Plot(b,x) ------ no computational complexity
Scalar - Matrix Addition 43 » a=3; » b=[1, 2, 3;4, 5, 6] b= 1 2 3 4 5 6 » c= b+a % Add a to each element of b c= 4 5 6 7 8 9
Scalar - Matrix Subtraction 44 » a=3; » b=[1, 2, 3;4, 5, 6] b= 1 2 3 4 5 6 » c = b - a %Subtract a from each element of b c= -2 -1 0 1 2 3
Scalar - Matrix Multiplication 45 » a=3; » b=[1, 2, 3; 4, 5, 6] b= 1 2 3 4 5 6 » c = a * b % Multiply each element of b by a c= 3 6 9 12 15 18
Scalar - Matrix Division 46 » a=3; » b=[1, 2, 3; 4, 5, 6] b= 1 2 3 4 5 6 » c = b / a % Divide each element of b by a c= 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000
The use of “.” – “Element” Operation 47 Given A: Divide each element of Multiply each Square each A by 2 element of A by 3 element of A
MATLAB Toolboxes 48 MATLAB has a number of add-on software modules, called toolbox , that perform more specialized computations. Signal Processing Image Processing Communications System Identification Wavelet Filter Design Control System Fuzzy Logic Robust Control -Analysis and Synthesis LMI Control Model Predictive Control …
MATLAB Demo 49 Demonstrations are invaluable since they give an indication of the MATLAB capabilities. A comprehensive set are available by typing the command >>demo in MATLAB prompt. demo
An Interesting, MATLAB command 50 why In case you ever needed a reason
Topics.. 51 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
Plot 52 Example PLOT Linear plot. x = [-3 -2 -1 0 1 2 3]; PLOT(X,Y) plots vector Y y1 = (x.^2) -1; versus vector X plot(x, y1,'bo-.'); PLOT(Y) plots the columns of Y versus their index PLOT(X,Y,S) with plot symbols and colors See also SEMILOGX, SEMILOGY, TITLE, XLABEL, YLABEL, AXIS, AXES, HOLD, COLORDEF, LEGEND, SUBPLOT... 52
Plot Properties 53 Example XLABEL X-axis label. ... xlabel('x values'); XLABEL('text') adds text ylabel('y values'); beside the X-axis on the current axis. YLABEL Y-axis label. YLABEL('text') adds text beside the Y-axis on the current axis. 53
Hold 54 Example HOLD Hold current graph. ... hold on; HOLD ON holds the current y2 = x + 2; plot and all axis properties so plot(x, y2, 'g+:'); that subsequent graphing commands add to the existing graph. HOLD OFF returns to the default mode HOLD, by itself, toggles the hold state. 54
Subplot 55 SUBPLOT Create axes in tiled positions. SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an m-by-n matrix of small axes Example x = [-3 -2 -1 0 1 2 3]; y1 = (x.^2) -1; % Plot y1 on the top subplot(2,1,1); plot(x, y1,'bo-.'); xlabel('x values'); ylabel('y values'); % Plot y2 on the bottom subplot(2,1,2); y2 = x + 2; plot(x, y2, 'g+:'); 55
Figure 56 FIGURE Create figure window. FIGURE, by itself, creates a new figure window, and returns its handle. Example x = [-3 -2 -1 0 1 2 3]; y1 = (x.^2) -1; % Plot y1 in the 1st Figure plot(x, y1,'bo-.'); xlabel('x values'); ylabel('y values'); % Plot y2 in the 2nd Figure figure y2 = x + 2; plot(x, y2, 'g+:'); 56
Surface Plot 57 x = 0:0.1:2; y = 0:0.1:2; [xx, yy] = meshgrid(x,y); zz=sin(xx.^2+yy.^2); surf(xx,yy,zz) xlabel('X axes') ylabel('Y axes') 57
3 D Surface Plot 58 contourf-colorbar-plot3-waterfall-contour3-mesh-surf 58
MATLAB Applications 59 DSP >> t=-2*pi:0.1:2*pi; y=1.5*sin(t); plot(t,y); xlabel('------> time') ylabel('------> sin(t)') 59
MATLAB Applications 60 DSP >> t=-2*pi:0.1:2*pi; y=1.5*cos(t); stem(t,y); xlabel('------> time') ylabel('------> sin(t)') 60
MATLAB Applications 61 DSP n=input('enter value of n') t=0:1:n-1; y1=ones(1,n); %unit step y2=[zeros(1,4) ones(1,n-4)]; %delayed unit step subplot(2,1,1); stem(t,y1,'filled');ylabel('amplitude'); xlabel('n----->');ylabel('amplitude'); subplot(2,1,2); stem(t,y2,'filled'); xlabel('n----->');ylabel('amplitude'); 61
MATLAB Applications 62 DSP 62
MATLAB Applications 63 Control Systems Transfer Function p1 s n + p 2 s n −1 + ... + p n +1 H (s ) = q1 s m + q1 s m −1 + ... + q m +1 where p1 , p 2 ... p n +1 numerator coefficients q1 , q1 ... q m +1 denominator coefficients 63
MATLAB Applications 64 Control Systems Transfer Function Consider a linear time invariant (LTI) single- input/single-output system y ''+ 6 y '+ 5 y = 4u '+ 3u Applying Laplace Transform to both sides with zero initial conditions Y ( s) 4s + 3 G ( s) = = 2 U ( s) s + 6s + 5 64
MATLAB Applications 65 Control Systems Transfer Function >> num = [4 3]; >> [num,den] = >> den = [1 6 5]; tfdata(sys,'v') >> sys = tf(num,den) num = Transfer function: 0 4 3 4s+3 den = ----------------- 1 6 5 s^2 + 6 s + 5 65
MATLAB Applications 66 Control Systems Zero-pole-gain model (ZPK) (s − p1)(s − p2 ) +... + (s − pn ) H (s ) = K (s −q1)(s −q2 ) +... + (s −qm ) where p1 , p2 ... pn+1 the zeros of H(s) q1,q1 ... qm+1 the poles of H(s) 66
MATLAB Applications 67 Control Systems Zero-pole-gain model (ZPK) Consider a Linear time invariant (LTI) single- input/single-output system y ''+ 6 y '+ 5 y = 4u '+ 3u Applying Laplace Transform to both sides with zero initial conditions Y (s) 4s + 3 4( s + 0.75) G (s) = = 2 = U ( s ) s + 6 s + 5 ( s + 1)( s + 5) 67
MATLAB Applications 68 Control Systems >> G=tf([4 3],[1 6 5]) >> [z,p,k]=zpkdata(G) Transfer function: z= 4s+3 [-0.7500] ------------- s^2 + 6 s + 5 p= [-5;-1] k= 4 68
MATLAB Applications 69 Control Systems >> bode(G) 69
MATLAB Applications 70 Control Systems >> rlocus(G) 70
MATLAB Applications 71 Control Systems >> nyquist(G) 71
MATLAB Applications 72 Control Systems >> step(G) 72
MATLAB Applications 73 Control Systems >> impulse(G) 73
MATLAB Applications 74 Communication >> t=0:pi/100:2*pi; >> x=sin(t); >> subplot(211);plot(t,x); >> Fc=1000; >> Fs=2000; >> y=ammod(x,Fc,Fs); >> subplot(212);plot(t,y); 74
MATLAB Applications 75 Communication 75
Online MATLAB Resources 76 www.mathworks.com/ www.mathtools.net/MATLAB www.math.utah.edu/lab/ms/matlab/matlab.html web.mit.edu/afs/athena.mit.edu/software/matlab/ www/home.html www.utexas.edu/its/rc/tutorials/matlab/ www.math.ufl.edu/help/matlab-tutorial/ www.indiana.edu/~statmath/math/matlab/links.html www-h.eng.cam.ac.uk/help/tpl/programs/matlab.html 76
Reference Books 77 Mastering MATLAB 7, D. Hanselman and B. Littlefield, Prentice Hall, 2004 Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers, R. Pratap, Oxford University Press, 2005. 77
Some More Web Resources 78 MATLAB Educational sites: http://www.eece.maine.edu/mm/matweb.html Yahoo! MATLAB Web site: dir.yahoo.com/Science/mathematics/software/matlab/ Newsgroup: comp.soft-sys.matlab 78
Thanks 79 Questions ??

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Matlab

  • 1. 1 C Language is Simplest.
  • 2. 2 What may be the size of the program for writing a C code that generates sin wave?
  • 3. 3 But we can do the same by only three lines.
  • 4. x=0.1:0.1:10; 4 b=sin(x); Plot(x,b) ------ no computational complexity
  • 5. 5 That is the beauty we have as an engineer. Name is MATLAB
  • 6. Recent Trends in Computational techniques for Engineering 6 Use of MATLAB in Engineering Prof. Ashish M. Kothari Department of Electronics & Communication Engineering Atmiya Institute of Technology & Science, Rajkot
  • 7. Topics.. 7 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
  • 8. Topics.. 8 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions
  • 9. MATLAB 9 “MATrix LABoratory” Powerful, extensible, highly integrated computation, programming, visualization, and simulation package Widely used in engineering, mathematics, and science
  • 10. MATLAB 10 Everything in MATLAB is a matrix !
  • 11. MATLAB- Starting & Quiting 11 Starting MATLAB On a Microsoft Windows platform, to start MATLAB, double-click the MATLAB shortcut icon on your Windows desktop. On Linux, to start MATLAB, type matlab at the operating system prompt. After starting MATLAB, the MATLAB desktop opens – see “MATLAB Desktop”. You can change the directory in which MATLAB starts, define startup options including running a script upon startup, and reduce startup time in some situations.
  • 12. MATLAB- Starting & Quiting 12 Quiting MATLAB To end your MATLAB session, select Exit MATLAB from the File menu in the desktop, or type quit in the Command Window.
  • 15. MATLAB Variable 15 Variable names ARE case sensitive Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer) Variable names must start with a letter followed by letters, digits, and underscores.
  • 16. MATLAB Variable 16 >> 16 + 24 no declarations needed ans = 40 >> product = 16 * 23.24 mixed data types product = 371.84 semi-colon suppresses output of >> product = 16 *555.24; the calculation’s result >> product product = 8883.8
  • 17. MATLAB Variable 17 >> clear clear removes all variables; >> product = 2 * 3^3; >> comp_sum = (2 + 3i) + (2 - 3i); clear x y removes only x and y >> show_i = i^2; complex numbers (i or j) require >> save three_things no special handling >> clear >> load three_things >> who save/load are used to Your variables are: comp_sum product show_i retain/restore workspace variables >> product product = 54 use home to clear screen and put >> show_i cursor at the top of the screen show_i = -1
  • 18. MATLAB Special Variables 18 ans Default variable name for results pi Value of π eps Smallest incremental number inf Infinity NaN Not a number e.g. 0/0 i and j i = j = square root of -1 realmin The smallest usable positive real number realmax The largest usable positive real number
  • 19. Topics.. 19 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
  • 20. Math & Assignment Operators 20 Power ^ or .^ e.g a^b or a.^b Multiplication * or .* e.g a*b or a.*b Division / or ./ e.g a/b or a./b or or . e.g ba or b.a NOTE: 56/8 = 856 - (unary) + (unary) Addition + a+b Subtraction - a-b Assignment = a=b (assign b to a)
  • 21. Other MATLAB symbols 21 >> prompt ... continue statement on next line , separate statements and data % start comment which ends at end of line ; (1) suppress output (2) used as a row separator in a matrix : specify range
  • 22. MATLAB Relational Operators 22 MATLAB supports six relational operators. Less Than < Less Than or Equal <= Greater Than > Greater Than or Equal >= Equal To == Not Equal To ~=
  • 23. MATLAB Logical Operators 23 MATLAB supports three logical operators. not ~ % highest precedence and & % equal precedence with or or | % equal precedence with and
  • 24. MATLAB Matrices 24 MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored. Vectors are special forms of matrices and contain only one row OR one column. Scalars are matrices with only one row AND one column
  • 25. MATLAB Matrices 25 A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows: » a_value=23 a_value = 23
  • 26. MATLAB Matrices 26 A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas): » rowvec = [12 , 14 , 63] rowvec = 12 14 63
  • 27. MATLAB Matrices 27 A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons): » colvec = [13 ; 45 ; -2] colvec = 13 45 -2
  • 28. MATLAB Matrices 28 A matrix can be created in MATLAB as follows (note the commas AND semicolons): » matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9] matrix = 1 2 3 4 5 6 7 8 9
  • 29. Extracting a Sub-Matrix 29 A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices and the rows and columns to extract. The syntax is: sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ; where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix.
  • 30. MATLAB Matrices 30 A column vector can be Here we extract column 2 extracted from a matrix. of the matrix and make a As an example we create a column vector: matrix below: » matrix=[1,2,3;4,5,6;7,8,9] » col_two=matrix( : , 2) matrix = col_two = 1 2 3 4 5 6 2 7 8 9 5 8
  • 31. MATLAB Matrices 31 A row vector can be Here we extract row 2 of extracted from a matrix. the matrix and make a As an example we create row vector. Note that a matrix below: the 2:2 specifies the second row and the 1:3 » matrix=[1,2,3;4,5,6;7,8,9] specifies which columns of the row. matrix = » rowvec=matrix(2 : 2 , 1 : 3) 1 2 3 4 5 6 rowvec = 7 8 9 4 5 6
  • 32. Topics.. 32 What is MATLAB ?? Basic Matrix Operations Script Files /M-files and Function Files Some more Operations and Functions Plotting functions ..
  • 33. Use of M-File 33 There are two kinds of M-files: Scripts, which do not accept input arguments or return output arguments. They operate on data in the workspace. Functions, which can accept input arguments and return output arguments. Internal variables are local to the function. Click to create a new M-File
  • 34. M-File as script file 34 Save file as filename.m Type what you want to do, eg. Create matrices If you include “;” at the end of each statement, result will not be shown immediately Run the file by typing the filename in the command window
  • 35. MATLAB Function File 35 function [a b c] = myfun(x, y) Write these two lines to a file myfun.m b = x * y; a = 100; c = x.^2; and save it on MATLAB’s path >> myfun(2,3) % called with zero outputs ans = 100 >> u = myfun(2,3) % called with one output u = 100 >> [u v w] = myfun(2,3) % called with all outputs u = 100 v = Any return value which is not stored in 6 an output variable is simply discarded w = 4
  • 36. Topics.. 36 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
  • 37. Some Useful MATLAB commands 37 who List known variables whos List known variables plus their size help >> help sqrt Help on using sqrt lookfor >> lookfor sqrt Search for keyword sqrt in m-files what >> what a: List MATLAB files in a: clear Clear all variables from work space clear x y Clear variables x and y from work space clc Clear the command window
  • 38. Some Useful MATLAB commands 38 what List all m-files in current directory dir List all files in current directory ls Same as dir type test Display test.m in command window delete test Delete test.m cd a: Change directory to a: chdir a: Same as cd pwd Show current directory which test Display directory path to ‘closest’ test.m
  • 39. MATLAB Logical Functions 39 MATLAB also supports some logical functions. xor (exclusive or) Ex: xor (a, b) Where a and b are logical expressions. The xor operator evaluates to true if and only if one expression is true and the other is false. True is returned as 1, false as 0. any (x) returns 1 if any element of x is nonzero all (x) returns 1 if all elements of x are nonzero isnan (x) returns 1 at each NaN in x isinf (x) returns 1 at each infinity in x finite (x) returns 1 at each finite value in x
  • 40. Matlab Selection Structures 40 An if - elseif - else structure in MATLAB. Note that elseif is one word. if expression1 % is true % execute these commands elseif expression2 % is true % execute these commands else % the default % execute these commands end
  • 41. MATLAB Repetition Structures 41 A for loop in MATLAB for x = array for ind = 1:100 b(ind)=sin(ind/10) end while loop in MATLAB while expression while x <= 10 % execute these commands end
  • 43. Scalar - Matrix Addition 43 » a=3; » b=[1, 2, 3;4, 5, 6] b= 1 2 3 4 5 6 » c= b+a % Add a to each element of b c= 4 5 6 7 8 9
  • 44. Scalar - Matrix Subtraction 44 » a=3; » b=[1, 2, 3;4, 5, 6] b= 1 2 3 4 5 6 » c = b - a %Subtract a from each element of b c= -2 -1 0 1 2 3
  • 45. Scalar - Matrix Multiplication 45 » a=3; » b=[1, 2, 3; 4, 5, 6] b= 1 2 3 4 5 6 » c = a * b % Multiply each element of b by a c= 3 6 9 12 15 18
  • 46. Scalar - Matrix Division 46 » a=3; » b=[1, 2, 3; 4, 5, 6] b= 1 2 3 4 5 6 » c = b / a % Divide each element of b by a c= 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000
  • 47. The use of “.” – “Element” Operation 47 Given A: Divide each element of Multiply each Square each A by 2 element of A by 3 element of A
  • 48. MATLAB Toolboxes 48 MATLAB has a number of add-on software modules, called toolbox , that perform more specialized computations. Signal Processing Image Processing Communications System Identification Wavelet Filter Design Control System Fuzzy Logic Robust Control -Analysis and Synthesis LMI Control Model Predictive Control …
  • 49. MATLAB Demo 49 Demonstrations are invaluable since they give an indication of the MATLAB capabilities. A comprehensive set are available by typing the command >>demo in MATLAB prompt. demo
  • 50. An Interesting, MATLAB command 50 why In case you ever needed a reason
  • 51. Topics.. 51 What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions Plotting functions ..
  • 52. Plot 52 Example PLOT Linear plot. x = [-3 -2 -1 0 1 2 3]; PLOT(X,Y) plots vector Y y1 = (x.^2) -1; versus vector X plot(x, y1,'bo-.'); PLOT(Y) plots the columns of Y versus their index PLOT(X,Y,S) with plot symbols and colors See also SEMILOGX, SEMILOGY, TITLE, XLABEL, YLABEL, AXIS, AXES, HOLD, COLORDEF, LEGEND, SUBPLOT... 52
  • 53. Plot Properties 53 Example XLABEL X-axis label. ... xlabel('x values'); XLABEL('text') adds text ylabel('y values'); beside the X-axis on the current axis. YLABEL Y-axis label. YLABEL('text') adds text beside the Y-axis on the current axis. 53
  • 54. Hold 54 Example HOLD Hold current graph. ... hold on; HOLD ON holds the current y2 = x + 2; plot and all axis properties so plot(x, y2, 'g+:'); that subsequent graphing commands add to the existing graph. HOLD OFF returns to the default mode HOLD, by itself, toggles the hold state. 54
  • 55. Subplot 55 SUBPLOT Create axes in tiled positions. SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an m-by-n matrix of small axes Example x = [-3 -2 -1 0 1 2 3]; y1 = (x.^2) -1; % Plot y1 on the top subplot(2,1,1); plot(x, y1,'bo-.'); xlabel('x values'); ylabel('y values'); % Plot y2 on the bottom subplot(2,1,2); y2 = x + 2; plot(x, y2, 'g+:'); 55
  • 56. Figure 56 FIGURE Create figure window. FIGURE, by itself, creates a new figure window, and returns its handle. Example x = [-3 -2 -1 0 1 2 3]; y1 = (x.^2) -1; % Plot y1 in the 1st Figure plot(x, y1,'bo-.'); xlabel('x values'); ylabel('y values'); % Plot y2 in the 2nd Figure figure y2 = x + 2; plot(x, y2, 'g+:'); 56
  • 57. Surface Plot 57 x = 0:0.1:2; y = 0:0.1:2; [xx, yy] = meshgrid(x,y); zz=sin(xx.^2+yy.^2); surf(xx,yy,zz) xlabel('X axes') ylabel('Y axes') 57
  • 58. 3 D Surface Plot 58 contourf-colorbar-plot3-waterfall-contour3-mesh-surf 58
  • 59. MATLAB Applications 59 DSP >> t=-2*pi:0.1:2*pi; y=1.5*sin(t); plot(t,y); xlabel('------> time') ylabel('------> sin(t)') 59
  • 60. MATLAB Applications 60 DSP >> t=-2*pi:0.1:2*pi; y=1.5*cos(t); stem(t,y); xlabel('------> time') ylabel('------> sin(t)') 60
  • 61. MATLAB Applications 61 DSP n=input('enter value of n') t=0:1:n-1; y1=ones(1,n); %unit step y2=[zeros(1,4) ones(1,n-4)]; %delayed unit step subplot(2,1,1); stem(t,y1,'filled');ylabel('amplitude'); xlabel('n----->');ylabel('amplitude'); subplot(2,1,2); stem(t,y2,'filled'); xlabel('n----->');ylabel('amplitude'); 61
  • 62. MATLAB Applications 62 DSP 62
  • 63. MATLAB Applications 63 Control Systems Transfer Function p1 s n + p 2 s n −1 + ... + p n +1 H (s ) = q1 s m + q1 s m −1 + ... + q m +1 where p1 , p 2 ... p n +1 numerator coefficients q1 , q1 ... q m +1 denominator coefficients 63
  • 64. MATLAB Applications 64 Control Systems Transfer Function Consider a linear time invariant (LTI) single- input/single-output system y ''+ 6 y '+ 5 y = 4u '+ 3u Applying Laplace Transform to both sides with zero initial conditions Y ( s) 4s + 3 G ( s) = = 2 U ( s) s + 6s + 5 64
  • 65. MATLAB Applications 65 Control Systems Transfer Function >> num = [4 3]; >> [num,den] = >> den = [1 6 5]; tfdata(sys,'v') >> sys = tf(num,den) num = Transfer function: 0 4 3 4s+3 den = ----------------- 1 6 5 s^2 + 6 s + 5 65
  • 66. MATLAB Applications 66 Control Systems Zero-pole-gain model (ZPK) (s − p1)(s − p2 ) +... + (s − pn ) H (s ) = K (s −q1)(s −q2 ) +... + (s −qm ) where p1 , p2 ... pn+1 the zeros of H(s) q1,q1 ... qm+1 the poles of H(s) 66
  • 67. MATLAB Applications 67 Control Systems Zero-pole-gain model (ZPK) Consider a Linear time invariant (LTI) single- input/single-output system y ''+ 6 y '+ 5 y = 4u '+ 3u Applying Laplace Transform to both sides with zero initial conditions Y (s) 4s + 3 4( s + 0.75) G (s) = = 2 = U ( s ) s + 6 s + 5 ( s + 1)( s + 5) 67
  • 68. MATLAB Applications 68 Control Systems >> G=tf([4 3],[1 6 5]) >> [z,p,k]=zpkdata(G) Transfer function: z= 4s+3 [-0.7500] ------------- s^2 + 6 s + 5 p= [-5;-1] k= 4 68
  • 69. MATLAB Applications 69 Control Systems >> bode(G) 69
  • 70. MATLAB Applications 70 Control Systems >> rlocus(G) 70
  • 71. MATLAB Applications 71 Control Systems >> nyquist(G) 71
  • 72. MATLAB Applications 72 Control Systems >> step(G) 72
  • 73. MATLAB Applications 73 Control Systems >> impulse(G) 73
  • 74. MATLAB Applications 74 Communication >> t=0:pi/100:2*pi; >> x=sin(t); >> subplot(211);plot(t,x); >> Fc=1000; >> Fs=2000; >> y=ammod(x,Fc,Fs); >> subplot(212);plot(t,y); 74
  • 75. MATLAB Applications 75 Communication 75
  • 76. Online MATLAB Resources 76 www.mathworks.com/ www.mathtools.net/MATLAB www.math.utah.edu/lab/ms/matlab/matlab.html web.mit.edu/afs/athena.mit.edu/software/matlab/ www/home.html www.utexas.edu/its/rc/tutorials/matlab/ www.math.ufl.edu/help/matlab-tutorial/ www.indiana.edu/~statmath/math/matlab/links.html www-h.eng.cam.ac.uk/help/tpl/programs/matlab.html 76
  • 77. Reference Books 77 Mastering MATLAB 7, D. Hanselman and B. Littlefield, Prentice Hall, 2004 Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers, R. Pratap, Oxford University Press, 2005. 77
  • 78. Some More Web Resources 78 MATLAB Educational sites: http://www.eece.maine.edu/mm/matweb.html Yahoo! MATLAB Web site: dir.yahoo.com/Science/mathematics/software/matlab/ Newsgroup: comp.soft-sys.matlab 78
  • 79. Thanks 79 Questions ??