Introduction to MATLAB

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Iran University of Science and Technology, Computer Engineering Department, Introduction to MATLAB Ehsan Adeli M. (eadeli@iust.ac.ir) 

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Outline > Introduction » MATLAB Environment > Getting Help » Vectors, Matrices, and Linear Algebra > Plotting > User Defined Functions » Image Manipulation and Processing » Audio Processing » Filters and Operations Multimedia Systems (eadeli@iust.ac.ir) 

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Introduction » MATLAB Stands for MATrix LABoratory. » The MATLAB environment allows the user to: » manage variables » import and export data » perform calculations » generate plots » develop and manage files for use with MATLAB. » A script can be made with a list of MATLAB commands like other programming language. ‎‘Multimedia Systems (eadeli@tust.ac.ir)‏ َم 

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Environment ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Getting Help > Type one of following commands in the command window: » help - lists all the help topic help topic - provides help for the specified topic * help command - provides help for the specified command » help help - provides information on use of the help command » helpwin - opens a separate help window for navigation » lookfor keyword - Search all M-files for keyword » Or simply press ‘F1’ and use the graphical help window. >5 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Variables » Variable names: » Must start with a letter » May contain only letters, digits, and the underscore » Matlab is case sensitive, i.e. one & OnE are different variables. * Matlab only recognizes the first 31 characters in a variable name. » when a semi-colon » >> tutorial = 1234; » >> tutorial = 1234 » ”;” is placed at the end of each command, the result is not displayed. re ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Variables (Cont’d) » Special variables: ans : default variable name for the result pi: m = 3.1415926.. eps: € = 2.2204e-( 016, smallest amount by which 2 numbers can differ. Inf or inf : ©, infinity NaN or nan: not-a-number » Commands involving variables: who: lists the names of defined variables whos: lists the names and sizes of defined variables clear: clears all variables, reset the default values of special variables. clear name: clears the variable name clc: clears the command window clf: clears the current figure and the graph window. 7 Multimedia Systems 

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Vectors > >> x =[ 0 0.25*pi 0.5*pi 0.75*pi pi ] gx O 0.7854 1.5708 2.3562 3.1416 > >>y =[ 0; 0 25*pi; 0 5*pi; 0 75*pi; ] ys 0 0.7854 1.5708 y 2.3562 3.1416 8 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Vectors (Cont’d) » Vector Addressing - A vector element is addressed in MATLAB with an integer index enclosed in parentheses. » >> x(3) » The colon notation may be used to address a block of elements (start : increment : end) start is the starting index, increment is the amount to add to each successive index, and end is the ending index. A shortened format (start : end) may be used if increment is 1. bse (1:3) ans = 0 0.7854 1.5708 » NOTE: MATLAB index starts at 1. >9 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Vectors (Cont’d) startiend create row vector x starting with start, counting by one, ending at end X = startincrementend veate row vector x starting with start, counting by increment, ending at or before end linspace(start, end, number) create row vector x starting with start, ending at end, having number elements length(x) y=x ‘Transpose conjugate of vector x dot (x, y) velurns the sealar dot product of the vector x and 3 10 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Example: Array Operations 5 f= [12534] » Scalar-Array Mathematics: 1 2 8 4 << ‏عم‎ 9*1 » Element-by-Element Array-Arra ‏دع‎ ‎Mathematics: 1 8 5 7 ِ >>x=[123]; Addition 5 Subtraction i 5 1: Multiplication oe eae Division 8 8 z= Exponentiation a 4 10 8 11 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Matrices > A Matrix array is two-dimensional, << ]12 3: 456 having both multiple rows and 12 123 multiple columns, similar to vector 4 5 8 arrays: << 0 2 ]24 6 1 35[ » It begins with [, and end with ] he spaces or commas are used to separate 8 3 elements in a row >> (2,3) » semicolon or enter is used to separate rows. a » Matrix Addressing: 6 * matrixname(row, column) >> h(:,1) » colon may be used in place of a row or column reference to select the entire ‏تت‎ ‎row or column. 2 12 ‘Multimedia Systems (eadeli@tust.ac.ir) 1 

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Matrices (Cont’d) zeros(n) returns a n xn matrix of zeros Zeros(m,n) returns am x n matrix of zeros ones(n) returns a n x n matrix of ones ones(m,n) returns a m x n matrix of ones size (A) for a m x n matrix A, returns the row vector [m,n] containing the number of rows and columns in matrix. length(A) returns the larger of the number of rows or columns in A. 13 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Matrices (Cont’d) B=‘ eye(n) ® returns an n x n identity matrix eye(m,n) > returns an m x n matrix with ones on the main diagonal and zeros elsewhere. C=A+tB C=A-B B=a<A, where a is a scalar. C=A*B B= inv(A), A must be a square matrix in this case. rank (A) > returns the rank of the matrix A. B=A*2 > squares each element in the matrix C=A* A> computes A*A, and A must be a square matrix. det (A), and A must be a square matrix. ‘Multimedia Systems (eadeli@tust.ac.ir) Transpose Identity Matrix Addition and subtraction Multiplication Matrix Multiplication Matrix Inverse Matrix Powers Determinant 14 

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Example, Linear Equations 3x, 10) -x b=| 5} -1) Solution by Matrix Inverse: — Solution by Matrix Division: Ax=b The solution to the equation ATAX = Atb Ax=b x= Ab can be computed using left division MATLAB: MATLAB: ‏دم جد 1-1-1 132-:32-1] عم حد‎ ]3 2-1-1832: 1-1-1: >> b=[ 10; 5; -1]; << b =[10: 5; -1]; >> x = inv(A)*b >> x =A\b X= x= ۱ 20000 20000 Answer: 5.0000 000 ‏و ,5 2 يك ,2- > بي‎ 2-6 Sapo ‏همه‎ 

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Plotting Plotting Curves: plot (x,y) - generates a linear plot of the values of x (horizontal axis) and y (vertical axis). semilogx (x,y) - generate a plot of the values of x and y using a logarithmic scale for x and 4 linear scale for y semilogy (x,y) - generate a plot of the values of x and y using a linear scale for x and a logarithmic scale for y. loglog(x.y) - generate a plot ofthe values of x and y using logarithmic scales for both xan Multiple Curves: plot (x. y..w, 2)- multiple curves can be plotted on the same graph by using multiple arguments in a plot command, The variables x, , w, and z are vectors, Two curves be plotted: y vs. x, and z vs. w. legend (‘string!’, ‘string2’,...) - used to distinguish between plots on the same graph Multiple Figures: figure (n) - used in creation of multiple plot windows. place this command before the plot() command, and the corresponding figure will be labeled as “Figure n” Elose - closes the figure n window. close all - closes all the figure windows. Subplots: subplot (m, n, p) - m by n grid of windows, with p specifying the current plot as the pth window 16 ‘Multimedia Systems (eadeli@tust.ac.ir) > 

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Plotting (Cont’d) Description Adds dashed grids lines at the tick marks removes grid lines (default) toggles grid status (off to on, or on to off) labels top of plot with text in quotes labels horizontal (x) axis with text ia quotes: labels vertical (y) axis with text is quotes ‘Multimedia Systems (eadeli@tust.ac.ir) Command gridon grid off grid title Ctoxt’) xlabel text’) ylabel (text’) 

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Flow Control is temperature > 100 disp (‘Too hot — equipment malfunctioning.’) if logical expression _ elseif temperature > 90 — commands disp (Normal operating range.’); end elseif (Below desired operating range.’) else disp (Too cold — turn off equipment.’) end switch expression case fest expression 1 commands case fest expression 2 commands otherwise commands end 18 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Loops for variable = expression for t = 1:5000 ۲ commands y(t) = sin (2*pi*t/10); end end EPs = 1; while expression. while ( 1+EPS) >1 commands EPS = EPS/2; end 2 EPS = 2*EPS » break - is used to terminate the execution of the loop. ‘Multimedia Systems (eadeli@tust.ac.ir) 

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M-Files » A M-file is a group of MATLAB commands. » MATLAB can open and execute the commands exactly as if they were entered at the MATLAB command window. ۶ To run the M-files, just type the file name in the command window. (make sure the current working directory is set correctly) 20 Multimedia Systems (eadeli@iust.ac.ir) 

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User Defined Functions » Add the following command in the beginning of your m-file: > function [output variables] = function_name (input variables); » Note that the file name should be the same as the function name. 21 Multimedia Systems (eadeli@iust.ac.ir) 

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Data types in MATLAB Double (64-bit double- precision floating point) Single (32-bit single- precision floating point) Int32 (32-bit signed integer) Int16 (16-bit signed integer) Int8 (8-bit signed integer) Uint32 (32-bit unsigned integer) Uint16 (16-bit unsigned integer) Uint8 (8-bit unsigned integer) Images in MATLAB < MATLAB can import/export several image formats BMP (Microsoft Windows Bitmap) GIF (Graphics Interchange Files) HDF (Hierarchical Data Format) JPEG (Joint Photographic Experts Group) PCX (Paintbrush) PNG (Portable Network Graphics) TIFF (Tagged Image File Format) XWD (X Window Dump) MATLAB can also load raw-data or other types of image data 

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Images in MATLAB * Binary images : {0,1} * Intensity images : [0,1] or uint8, double etc. * RGB images : m-by-n-by-3 * Indexed images : m-by-3 color map * Multidimensional images m-by-n-by-p (p is the number of layers) 

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Image import and export » Read and write images in Matlab >> I=imread(‘cells.jpg'); >> imshow(1) >> size(I) ans= 479 600 3 (RGB image) >> Igrey=rgb2gray(1); >> imshow(Igrey) >> imwrite(Igrey, ‘cell_gray.tif’, 'tiff) Alternatives to imshow >>imagesc(1) >>imtool(1) >>image(!) 

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Images and Matrices > How to build a matrix (or image)? >>A=[123;456;789]; A=1 2 3 4 5 6 7 8 9 >> B = zeros(3,3) B= 0 0 0 0 0 0 0 0 0 >> C = ones(3,3) C= 1 1 1 1 1 1 1 1 1 >>imshow(A) (imshow(A,[]) to get automatic pixel range) 

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Image format conversion » Convert between intensity/indexed/RGB to binary format: dither() » Convert between intensity format to indexed format: gray2ind() » Convert between indexed format to intensity format: ind2gray() » Convert between indexed format to RGB format: ind2rgb() » Convert a regular matrix to intensity format by scaling: mat2gray() » Convert between RGB format to intensity format: rgb2gray() » Convert between RGB format to indexed format: rgb2ind() > 26 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Colormaps » I = imread (‘lena.bmp’); > imshow (I); » colormap (cool); » Autumn, bone, colorcube, cool, copper, flag, gray, hot, hsv, jet, pink, prism, spring, summer, white, winter 27 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Video >» mov = aviread(filename) >» mov = aviread(filename, index) > fileinfo = aviinfo(filename) Multimedia Systems (eadeli@iust.ac.ir) 

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Digital Audio cP ae y y Micon 9 Digi Sigua | Voltage Wave! vol vo My be 1s1g2 conde > 29 ‘Multimedia Systems (eadeli@tust.ac.ir) 

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Audio > [road,fs]=wavread('road.wav'); » The array road now contains the stereo sound data and fs is the sampling frequency. > This data is sampled at the same rate as that on a music CD (fs=44,100 samples/second). > The left and right channel signals are the two columns of the road array: > left=road(:,1); > right=road(:,2); 30 

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> time=(1/44100)*length(left); » t=linspace(0,time,length(left)); > plot(t,left) > xlabel('time (sec)'); » ylabel(‘relative signal strength’) > soundsc(left,fs) % plays left channel as mono » soundsc(right,fs) % plays right channel mono (sound nearly the same) > soundsc(road,fs) % plays stereo (ahhh...) 31 Multimedia Systems (eadeli@iust.ac.ir)