Basics of MATLAB and Beyond

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clfpolar(t,gdb)In this case you must use a modified version of polar that interpretsa zero radius as a 0 dB value which should go at the outer limit of theplot. Negative decibel values should appear at smaller radii. I haveimplemented these ideas in the m-file negpolar (see companion software):negpolar(t,gdb)The negpolar function also omits the solid outer circle which, like thebox drawn around matlab’s default plot output, unnecessarily framesthe plot and can obscure the data that you are trying to display. A faintdotted grid is enough to put the plotted points in context. I will saymore about this in the section on Handle Graphics later (see page 65).17 Fourier TransformA theorem of mathematics says, roughly, that any function can be representedas a sum of sinusoids of different amplitudes and frequencies. TheFourier transform is the mathematical technique of finding the amplitudesand frequencies of those sinusoids. The Discrete Fourier Transform(DFT) is an algorithm that calculates the Fourier transform for numericaldata. The Fast Fourier Transform is an efficient implementation ofthe DFT. The following functions are available in matlab to do Fouriertransforms and related operations:c○ 2000 by CRC Press LLC
fftfft2fftnfftshiftifftifft2ifftnabsanglecplxpairnextpow2unwrapOne-dimensional fast Fourier transformTwo-dimensional fast Fourier transformN-dimensional fast Fourier transformMove zeroth lag to centre of transformInverse one-dimensional fast Fourier transformInverse two-dimensional fast Fourier transforminverse N-dimensional fast Fourier transformAbsolute value (complex magnitude)Phase angleSort complex numbers into complex conjugate pairsNext power of twoCorrect phase anglesThe FFT of the column vectory = [2 0 1 0 2 1 1 0]’;is>> Y = fft(y)Y =7.0000-0.7071+ 0.7071i2.0000- 1.0000i0.7071+ 0.7071i5.00000.7071- 0.7071i2.0000+ 1.0000i-0.7071- 0.7071iThe first value of Y is the sum of the elements of y, and is the amplitudeof the “zero-frequency”, or constant, component of the Fourier series.Terms 2 to 4 are the (complex) amplitudes of the positive frequencyFourier components. Term 5 is the amplitude of the component at theNyquist frequency, which is half the sampling frequency. The last threeterms are the negative frequency components, which, for real signals, arecomplex conjugates of the positive frequency components.The fftshift function rearranges a Fourier transform so that thenegative and positive frequencies lie either side of the zero frequency.Companion M-Files Feature 4 The function fftfreq givesyou a two-sided frequency vector for use with fft and fftshift.For example, the frequency vector corresponding to an 8-pointFFT assuming a Nyquist frequency of 0.5 is>> fftfreq(.5,8)’ans =c○ 2000 by CRC Press LLC
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BASICS OFMATLAB®and Beyondc○ 200
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Library of Congress Cataloging-in-P
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typing pwd (print working directory
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ContentsIBasics of MATLAB1 First St
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20 Time-Frequency Analysis21 Line A
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39Answers to Exercises (Part I)40 A
Page 14 and 15: Set → Getting Started with MATLAB
Page 16 and 17: 1.5 The Colon OperatorTo generate a
Page 18 and 19: matlab will recall the last command
Page 20 and 21: a = zeros(2,3)a =0 0 00 0 0>> b = o
Page 22 and 23: [a a(a)]ans =1 2 3 1 4 74 5 6 2 5 8
Page 24 and 25: a + bans =11 3344 6677 993.8 Transp
Page 26 and 27: 4.2 Adding PlotsWhen you issue a pl
Page 28 and 29: x = [[1 2 3 4]’ [2 3 4 5]’ [3 4
Page 30 and 31: 4.7 AxesSo far we have allowed matl
Page 32 and 33: v =1122>> v*uans =1 2 0 11 2 0 12 4
Page 34 and 35: max returns a vector containing the
Page 36 and 37: s = 100*spiral(3)s =700 800 900600
Page 38 and 39: We can plot the surface z as a func
Page 40 and 41: The contour function plots the cont
Page 42 and 43: m = gray(8);colormap(m)imagesc(1:10
Page 44 and 45: hold onplot3(x(ind),y(ind),z(ind),
Page 46 and 47: z = 5*ones(3,3)z =5 5 55 5 55 5 5>>
Page 48 and 49: contour(x,y,z,30);You may have noti
Page 50 and 51: variables that are local to themsel
Page 52 and 53: SwitchThe basic form of a switch st
Page 54 and 55: i =i =123136Vectorised Codematlab i
Page 56 and 57: 9.1 MATLAB FormatTo save all the va
Page 58 and 59: 11 StartupEach time you start matla
Page 60 and 61: Where p i is the population for yea
Page 62 and 63: NaNs by leaving them off the plot.
Page 66 and 67: -0.5000-0.3750-0.2500-0.125000.1250
Page 68 and 69: the periodograms of the blocks, and
Page 70 and 71: plot(y(1:1000))axis([0 1000 -5 5])z
Page 72 and 73: comet(x,y)(You can get a three-dime
Page 74 and 75: By clicking within the panner box a
Page 76 and 77: x = linspace(-1,1,8192);Fs = 1000;y
Page 78 and 79: 23.3 Graphical Object Hierarchymatl
Page 80 and 81: Now we need to get the handles of a
Page 82 and 83: Beyond the BasicsPreludeThis part o
Page 84 and 85: clfgplot(A,[x y])axis off(Try zoomi
Page 86 and 87: str =you’re the one>> str = ’
Page 88 and 89: strrep(str,’go’,’am’)ans =I
Page 90 and 91: ans =3.14159e+100Some additional te
Page 92 and 93: eval(str)v =1 2 3 4 5The eval(str)
Page 94 and 95: Inline objects, like every other ma
Page 96 and 97: a(1,1) = {[1 2 3]}a =[1x3double]or>
Page 98 and 99: t = {’help’ spiral(3) ; eye(2)
Page 101 and 102: meteo.Temperatureans =24ans =19.000
Page 103 and 104: 3 >> a = [1 2 ;4 5 6;7 8 9]a =1 2 3
Page 105 and 106: [x,y] = meshgrid(1:5,1:3)x =1 2 3 4
Page 107 and 108: ans(:,:,2) =999And to sum over “p
Page 109 and 110: An Application of RGB ImagesTo see
Page 111 and 112: You can see that over the 8 time st
Page 113 and 114: name>> staff(2,1,2).name(5:9)ans =B
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q =7 8 96 1 25 4 3>> save saved_dat
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fid = fopen(’asc.dat’);The fope
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display and the enclosed area is th
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MarkerEdgeColor = auto(and so on)In
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text(-.7,f(-.7),’f(X)’)But we h
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plt(x,f(x/2),’--’)Let us try ca
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Example: findobjThe findobj command
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3. Add the property you want to set
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is numbered from top to bottom. The
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axis ijUsually images like this do
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32.2 Tick Marks and Labelsmatlab’
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clfaxes(’pos’,[.2 .1 .7 .4])x =
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property to [0 top] in the call to
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object’s HorizontalAlignment and
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the required symbols. The m-file ti
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1. Use graphical elements that serv
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uicontrol(’Callback’,’ezplot(
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uicontrol(’Pos’,[110 280 60 19]
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’String’,’0.5’,’Style’,
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function exradio(action)if nargin =
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fail. One place to put variables th
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34.7 Fast DrawingFor fast drawing o
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controlled by guide and which are a
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InvertHardcopy: [ {on} | off ]Paper
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Another option is to use an image f
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yur is the y coordinate of the uppe
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\end{center}\caption{This is the fi
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x 294x1 ...y 294x1 ...z 294x1 ...Gr
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diagram. Such a triangular grid can
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xt = x([1 9 10 1]);yt = y([1 9 10 1
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x = [0 0 .5 0.5 .5 1 11 .5 .5 .5];y
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fac2 = [1 2 61 6 31 4 61 6 5];The r
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t = linspace(0,2*pi,20);x = cos(t);
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N = 20;dt = 2*pi/N;t = 0:dt:(N-1)*d
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colouring of the sphere itself. To
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material dullThe default is materia
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time taken by this routine to calcu
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first row of a by taking the column
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38.3 Debuggingmatlab has a suite of
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10: y = linspace(ycentre - L,ycentr
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We change variables:p ′ = C + Bx.
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Exercise 6 (Page 59)You can generat
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33 ! 36 $ 39 ’ 42 * 45 - 48 034 "
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R = 1; N = 200;[x,y] = meshgrid(lin
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(The plot might take a few seconds
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% Reproduce the layers at the diffe
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