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added Analogtechnik added PCBWay to manufacturers
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Simon M. Burkhardt
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Nov 17, 2018
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%****************************************************************************** | ||
% \details : An3E Serie 1 | ||
% \autor : Simon Burkhardt | ||
% \file : An3E_Mehrdimmensionale_Analysis_Grundlagen.m | ||
% \date : 17.11.2018 | ||
% \version : 1.0 | ||
%****************************************************************************** | ||
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%% Grundlagen | ||
clear all; close all; clc; format shorteng | ||
% x-Koordinaten des Gitters | ||
% in 1er schritten von -3 bis 3 | ||
x = -3:1:3; | ||
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% y-Koordinaten | ||
y = -1:0.5:1; | ||
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% Erstellen eines Gitternetzes | ||
[X Y] = meshgrid(x,y); | ||
[X Y] = meshgrid(-10:0.5:10); | ||
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Z = 100 - X.^2 - Y.^2; | ||
% mesh(X,Y,Z); | ||
surf(X,Y,Z); | ||
xlabel x | ||
ylabel y | ||
zlabel z | ||
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%% Beispiel S. 27 | ||
clear all; close all; clc; format shorteng | ||
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x = -2:0.1:2; | ||
y = -2:0.1:2; | ||
[X Y] = meshgrid(x, y); | ||
Z = X.*exp(-X.^2-Y.^2); | ||
surf(X,Y,Z); | ||
xlabel x | ||
ylabel y | ||
zlabel z | ||
colormap hot | ||
%% | ||
colormap parula | ||
colormap jet | ||
colormap hsv | ||
colormap hot | ||
colormap cool | ||
colormap spring | ||
colormap summer | ||
colormap autumn | ||
colormap winter | ||
colormap gray | ||
colormap bone | ||
colormap copper | ||
colormap pink | ||
colormap lines | ||
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map = [1 1 0 | ||
1 0.5 0 | ||
1 0 0 | ||
1 0 0.5 | ||
0.5 0 0.5 | ||
0.1 0 0.1 | ||
0 0 0]; | ||
colormap(map) | ||
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% https://www.mathworks.com/matlabcentral/fileexchange/40318-build-custom-colormaps | ||
[cmap] = buildcmap('kbry'); % black-blue-red-yellow | ||
colormap(cmap) | ||
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%% Beispiel S. 34) | ||
clear all; close all; clc; format shorteng | ||
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x = -6:0.1:6; | ||
y = -5:0.1:5; | ||
[X Y] = meshgrid(x, y); | ||
Z = -X.^2+Y.^2-2.*Y; | ||
contour(X,Y,Z, [-3 -2 -1 0 1]); | ||
grid on | ||
map = [0 0 0.7 | ||
0 0.7 0 | ||
0 0 0 | ||
0.7 0 0 | ||
0 0 0]; | ||
colormap(map) | ||
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%% Beispiel S. 35 | ||
clear all; close all; clc; format shorteng | ||
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x = -5:0.1:5; | ||
y = -5:0.1:5; | ||
[X Y] = meshgrid(x, y); | ||
Z = sin(X)+2.*sin(Y); | ||
contour(X, Y, Z); | ||
%% | ||
clear all; close all; clc; format shorteng | ||
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[X Y] = meshgrid(-5:0.1:5); | ||
Z = sin(X)+2.*sin(Y); | ||
surfc(X, Y, Z); |
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Original file line number | Diff line number | Diff line change |
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%****************************************************************************** | ||
% \details : An3E Serie 1 | ||
% \autor : Simon Burkhardt | ||
% \file : An3E_Serie_1.m | ||
% \date : 22.09.2018 | ||
% \version : 1.0 | ||
%****************************************************************************** | ||
clear all; clc | ||
format shorteng | ||
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%% | ||
% 1) | ||
syms x; | ||
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f_a = log(x+1); | ||
f_a_dx = diff(f_a, x); | ||
% 1/(x + 1) | ||
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f_b = 1/2 * asin(x)^2; | ||
f_b_dx = diff(f_b, x) | ||
% asin(x)/(1 - x^2)^(1/2) | ||
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f_c = -1/4 * (x-1)^4; | ||
f_c_dx = diff(f_c, x) | ||
% -(x - 1)^3 | ||
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%% | ||
% 2) | ||
clear; clc; | ||
syms x t; | ||
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f_a = (1-t)^3; | ||
Ff_a_t = int(f_a, t) | ||
% -(t - 1)^4/4 | ||
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f_b = exp(x)*cos(t); | ||
Ff_b_x = int(f_b, x) | ||
%exp(x)*cos(t) | ||
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f_c = f_b; | ||
Ff_c_t = int(f_c, t) | ||
%exp(x)*sin(t) | ||
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f_d = x^2*exp(-x); | ||
Ff_d_x = int(f_d, x) | ||
% -exp(-x)*(x^2 + 2*x + 2) | ||
lsg_d = int(f_d, x, 0, 10) | ||
% 2 - 122*exp(-10) | ||
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%% | ||
% Serie 1b | ||
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%% | ||
% 2) | ||
clear; clc; | ||
syms x n pi; | ||
assume(n, 'integer'); | ||
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f_x = abs(x) * (pi - abs(x)); | ||
a0 = 1/pi * int(f_x, x, -pi, pi) | ||
% vpa(a0) | ||
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%a(n) = 1/pi * int(abs(x) * (pi - abs(x))*cos(n*x), x, -pi, pi); | ||
%simplify(a(n)) | ||
% abs(x) * (pi - abs(x)) | ||
a(n) = 1/pi * int(f_x *cos(n*x), x, -pi, pi); | ||
an = simplify(a(n)) | ||
pretty(an) | ||
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b(n) = 1/pi * int(f_x *sin(n*x), x, -pi, pi); | ||
bn = simplify(b(n)) | ||
pretty(bn) | ||
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%% | ||
clear; clc; | ||
syms x n pi; | ||
assume(n, 'integer'); | ||
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f_x = x; | ||
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a0 = 1/pi * int(f_x, x, 0, 2*pi) | ||
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a(n) = 1/pi * int(f_x * cos(n*x), x, 0, 2*pi); | ||
b(n) = 1/pi * int(f_x * sin(n*x), x, 0, 2*pi); | ||
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an = simplify(a(n)) | ||
pretty(an) | ||
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bn = simplify(b(n)) | ||
pretty(bn) | ||
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%% | ||
clear; clc; | ||
syms x; | ||
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f_x = x^2; | ||
%ezplot(f_x, [0, 2*pi]); | ||
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syms n pi; | ||
assume(n, 'integer'); | ||
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a0 = 1/pi * int(f_x, 0, 2*pi) | ||
pretty(a0) | ||
a(n) = 1/pi * int(f_x*cos(n*x), x, 0, 2*pi); | ||
b(n) = 1/pi * int(f_x*sin(n*x), x, 0, 2*pi); | ||
an = simplify(a(n)) | ||
pretty(an) | ||
bn = simplify(b(n)) | ||
pretty(bn) | ||
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%% | ||
clear; clc; close all; | ||
x = linspace(0, 3*pi, 1e3); %% Periodendauer T anpassen | ||
y = zeros(1, 1e3); | ||
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% Fourier Koeffizienten und original Funktion angeben | ||
a0 = 8*pi^2/3; | ||
a = @(n) 4/(n^2); | ||
b = @(n) -4*pi/n; | ||
f_x = @(x) mod(x, 2*pi).^2; | ||
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% a0 = pi^2/3; | ||
% a = @(n) -2/(n^2)*(1+(-1)^n); | ||
% b = @(n) n^0 -1; | ||
% f_x = @(x) abs(x).*(pi-abs(x)); | ||
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for m=1:1e3 | ||
y(m) = a0/2; % a0 setzen | ||
end | ||
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for n=1:10 % Anzahl Glieder in der Summierkette | ||
y = y + a(n).*cos(n.*x) + b(n).*sin(n.*x); | ||
end | ||
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plot(x, y); % Fourier Plot | ||
hold on; | ||
plot(x, f_x(x)); % original Plot | ||
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