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Lecture: Introduction to DSP simulations in MATLAB

Lecture: Introduction to DSP simulations in MATLAB 1
SGN1158 Introduction to Signal Processing, short version Lecture: Introduction to DSP simulations in MATLAB Konstantin Rykov konstantin.rykovtut.fi • Why you’re at this lecture/lab • Do not fear MATlab. It’s your friend • MATlab is a tool • Where I can use MATlab Examples • I’m afraid of program languages… • THE MAIN IDEA OF THE LECTURE 11.9.2012 2 Сontents BASICS OF MATLAB • Mainwindow. How to make mfile How to save mfile • Some basic hints • Main MATLAB objects (commands, variables…) • Main operation symbols • Operation symbols MATLAB IS AN ADVANCED CALCULATOR • Complex numbers • HELP • Vectors • Matrices 2D GRAPHS • Main MATLAB functions for plotting graphs • General rules of forming graphs • Main tools of staging graphs • Controlling graph properties • LineSpec parameters OUTER FUNCTIONS IN MATLAB 11.9.2012 3 Сontents DISCRETE SIGNALS IN MATLAB • Sequences • Unit sample sequence, unit step sequence, discrete exp • Discrete complex harmonic signal • Functions max, sum and prod • Generation of signals: rectpuls, tripuls, gauspuls, sinc, square, sawtooth, diric • Functions rand(1,N) and randn(1, N) • TASK: Open MATLAB 11.9.2012 4 BASICS OF MATLAB The main MATLAB window 11.9.2012 5 Some basic hints • help name (for example: help cos) • ; blocks automatically output of the variables • makes a comment • to comment a few rows hold Ctrl+R • to uncomment a few rows Ctrl+T • Always use: clc,clear all; close all; TASK • Type in Editor: • =============== • My MATlab Crib • =============== • Use CTRL+R to comment it • clc; clear all; close all; 11.9.2012 6 Main MATLAB objects • Commands (clc, help, demo) • Constants (10, 17.28, 5+3j, 1e6, 102) • Standard const (pi, 1i, eps) • Variables – MATlab object, which might change it’s value during simulation. All variables are MATRIXES in MATlab • Functions (sin(X), exp(X), log10(X), sqrt(X), abs(X), real(X), imag(X)) • Expressions – is a sum of constants, functions, variables, which are summed by operational symbols (x+sin(a)sqrt(pi);) 11.9.2012 7 Main operation symbols Symbol Operation + Summation Difference Multiplication of matrixes . Multiplication of elements / Right division .’ Transposing 11.9.2012 8 MATLAB IS AN ADVANCED CALCULATOR Complex numbers Use MATLAB as calculator to find answers 11.9.2012 9 Use help to find what these commands do • abs • angle • exp • conj 11.9.2012 10 Type and simulate • z=3+4i • r=abs(z) • fii=angle(z) • rexp(ifii) • zk=conj(z) • zzkr2 • What the command format does 11.9.2012 11 Vectors • Type a=2 4 5 7 and b=1 4 2 1 • Find a+b, 2a2b • What happens if you type a’ and b’ • ab; a’b; ab’; a’b’; • 1:10; 0:2:100; 1:0.25:2 • Form vectors a=(7,8,9,…,22); b=(0,2,4,…,100); c=(100,95,90,…,35) • What did you get a(3) a(3 5 7) a(3:7) a(3:end) 11.9.2012 12 Matriсes A=7 5 9; 2 1 2; 1 1 2; 11.9.2012 13 Task • Calculate: 3A5C, 7A+2B, CA, CD’ • Find out commands: zeros(n), zeros(m,n), ones(n), ones(m,n), size(D), zeros(size(D)), diag(1 2 3 4), eye(n) • What happens A,B and A;B • Try to find an easy way to build a 78matrix whose other entries are zeros, but in its diagonal and its last column are 5s NOTE: Transpose of a matrix is obtained with command – ’ • row with A(i,:) and column with A(:,j) 11.9.2012 14 • Determine whether the given sets of vectors are linearly independent/dependent: W1=1 2 3, W2=2 1 5, W3=1 2 4, W4=0 2 1 • Use MATLAB to to choose randomly three three column vectors in The MATLAB commands to choose these vectors are: • y1=rand(3,1) • y2=rand(3,1) • y3=rand(3,1) HINT check the command rref 11.9.2012 15 2D GRAPHS Main MATLAB functions for plotting graphs Function Meaning plot (x1, y1, x2, y2,…) Linear graphics stem Sequence graphs stairs Stairs graphs loglog Both Logarithmic axis Im and Re semilogx Logarithmic Re axis semiloxy Logarithmic Im axis 11.9.2012 16 General rules of forming graphs • figure – making a new window for a graph • subplot (n,m,p) – drawing a few graphs in one window: n – colum, m – row, p – ordinal number of the graph • hold on – plotting another graph at the same picture • hold off • For more information help graph2d 11.9.2012 17 Generate x=1 20 3 15 18; Use functions and tell what is the difference: • plot • stem Generate x1=0:pi/8:8pi. What we have done Generate y(t)=sin(x). Use functions to plot graphs: • plot • stem • stairs • HINT: use command figure or function subplot(n,m,p) 11.9.2012 18 Use semilogx, semilogy, loglog to plot graphs of the following functions: 1. y=3x5 2. y=3(5x2) 3. y=log10(3x4) • Use subplot command into 33subplot as described bellow ‘case (1) semilogx’ ‘case (1) semilogy’ ‘case(1) loglog’ ‘case (2) semilogx’ ‘case (2) semilogy’ ‘case(2) loglog’ ‘case (3) semilogx’ ‘case (3) semilogy’ ‘case(3) loglog’ • Consider again y=3x5. Use plot(x,log10(y)) and compare its plot with semilogy plot. What is the difference and similarity between them 11.9.2012 19 Main tools of staging graphs Function grid title(‘text’) xlabel (‘text’) ylabel (‘text’) Legend (‘funct1’,’funct2’,..,Pos) axis(XMIN XMAX YMIN YMAX) xlim (XMIN XMAX) ylim (YMIN YMAX) Pos (1, 0, 1,…,4) TRY THEM 11.9.2012 20 Generate x1=0:pi/8:8pi; y1=sin(x1); Form 3 graph in 1 window. st • 1 graph: plot a discrete signal y(x) nd • 2 graph: plot a discrete signal. Use axis(0 10 1 1) • 3rd graph: do the same, but limit Re axis and Im axis by using xlim(15 15) and ylim(1.5 1.5) For all graphs: make a grid, title and give names for both axis Generate y2=0.5sin(2x1); plot(x1,y1,x1,y2),legend(‘sin(x1)’,’0.5sin(2x1)’); HINT: use hold on 11.9.2012 21 Controlling grpah properies Each function has different properties. • plot(x1,y1,…,LineSpec,’PropertyName’,PropertyValue,…); • stem(x1,y1,…,LineSpec,’fill’,’MarkerSize’,3); PropertyName is divided into: • LineWidth – line width; • MarkerEdgeColor – marker color ; • MarkerFaceColor – color by which the marker is filled; • MarkerSize – size of the marker , give a value (default 7). Let us divide LineSpec parameters into 3 groups: s1, s2, s3. 11.9.2012 22 LineSpec parameters S1 S2 S3 r Red + b Blue : g Green . s Square w White d Diamond k Black (none) v y Yellow m Magenta c Cyan p Pentagram h Hexagram 11.9.2012 23 • Form a vector y = 0 1 2 3 4 5 6 7 8 9; line width is 2, use squared black markers, dotted line • x1=0:pi/8:8pi; y1=sin(x1); line width 3, dashdot line, filled green markers, marker size 5 • y1=sin(x1); y2=0.2cos(5x1); one line is dashed, another is solid; one line is red, another is green; markers, different sizes 11.9.2012 24 OUTER FUNCTIONS IN MATLAB Function file – is a Mfile, which generates outer function DO NOT PUT ; after function row After function there is a function body Put ; everywhere in the body to prevent undesirable output Good programming means good comments 11.9.2012 25 • If you have a few parameters function z, p = F1(x,y) Sum of cubes z Square root p z=x.3+y.3; p=sqrt(abs(z)); end • If you have one parameter function z = F2(x,y) Sum of cubes z z=x.3+y.3; end • After making and saving functionfile you can use it in other Mfiles (script files). • Actual/Real parameters a=4, b=3, d,c=F1(a,b) = saved in Workspace • Formal parameters 3+5sqrt(9) = not saved in Workspace 11.9.2012 26 Number of input and output parameters can be formed by commands: • nargin(’function name’) • nargout(’function name’) Listing of the function is formed by command: • type name of functionfile If you need commends of the function file: • help name of functionfile If you need to exit compulsory from the body of the outer function use operator: • return 11.9.2012 27 Let us remake function F1 to F3 with controlling negative argument of the square root and appropriation p=0 in this case: function z, p = F3(x,y) Sum of cubes z Square root p z=x.3+y.3; if z0 p=0; return else p=sqrt(z); end end 11.9.2012 28 DESCRETE SIGNALS IN MATLAB Sequences • What is a discrete signal How does it look like • How to make a discrete signal: • Matrix x=0 1; 4 7; 3 2; • Vector y=1 20 3 15 18; • Pair of vectors n1=0:12; x1=n.2; • Vector+Matrix n2=0:2; x2=0 1; 4 7; 3 2; 11.9.2012 29 10 20 15 5 10 0 5 5 0 1 1.5 2 2.5 3 1 2 3 4 5 n n 150 10 100 5 50 0 0 5 0 5 10 15 0 0.5 1 1.5 2 n n 11.9.2012 30 Unit sample sequence, unit step sequence, discrete exp, Form a unit sample sequence, unit step sequence and discrete exp. The length of the sequence is N=11. Plot graphs. 11.9.2012 31 Discrete complex harmonic signal is presented as or , where Fs=1/T. Real and imaginary parts of x(n) are calculated by functions real and imag. Absolute value and angle/phase can be hound with the use of abs and angle Now, present 32 samples of DCHS x(n), if C=2 and w=pi/8. Plot real, imaginary parts of the signal. Present absolute value and the phase of x(n). 11.9.2012 32 Functions max, sum and prod We can work only with vectors/matrices, which have the same length/dimentions. Generate 3 signals x1=(0.8.n1), x2=cos(wn2) and x3=sin(wn3) with vector length correspondingly N1=16, N2=24, N3=32 and w=pi/8. N=max(N1 N2 N3) – to find the maximum value of the vector length. To add the needed number of zeros to the signal: y1=x1 zeros(1, (NN1));… Use sum to summate signals and prod to multiply signals. Check commands if needed in help. 11.9.2012 33 Generation of signals: rectplus, triplus, gausplus, sinc, square, sawtooth, diric There is a number of functions for generating signals in the folder Signal Processing Toolbox. y=rectpuls(t,w); y=tripuls(t,w,s); y=gauspuls(t,fc, bw); y=sincpuls(t); y=squarepuls(t,d); y=sawtoothpuls(t,width); y=diricpuls(x,N); 11.9.2012 34 Functions rand(1, N) and randn(1, N) RAND is a uniformly distributed pseudorandom number. RANDN is a normally distributed pseudorandom numbers. (1, N) – number of rows and columns. Form additive mixture (sum) of sequence x(n)=sin(wn) with the length N=32 with white noise: uniformly distributed and normally distributed. 11.9.2012 35 Thanks for attention Questions 11.9.2012 36