MATLAB Answers

Plotting the derivative of an "switch-funktion"

조회 수: 3(최근 30일)
Jann B
Jann B 6 Apr 2020
댓글: Jann B 16 Apr 2020
Hello,
we got some switch funktions which i plotted with the code shown below.
The only thing i need to fix, is the plot of the derivative of these funktion.
Where the dirac should be shown (just a peak), nothing appears.
Can someone give me a hint?
Thank you in advance.
%% ÜA Karlsruhe
% 2
% 2.1
clc, clear, clf
set(0,'DefaultFigureWindowStyle','docked')
% Signal A
figure('Name', 'RT_Karlsruhe 2.1', 'NumberTitle', 'off')
subplot(4, 1, 1)
hold on, grid on, axis equal
start = -2;
ende = 10;
t = linspace(start,ende,5000);
a = @(t) (t-2).*(heaviside(t-2) - heaviside(t-4)) + (t-6).*(heaviside(t-4) - heaviside(t-6));
A = a(t);
a_derivative = @(t) heaviside(t-2) - 4*dirac(t-4) - heaviside(t-6);
A_derivative = a_derivative(t);
syms x
diff_test = diff((x-2).*(heaviside(x-2) - heaviside(x-4)) + (x-6).*(heaviside(x-4) - heaviside(x-6)));
% x = t;
%
% Diff_test = diff_test(x);
plot(t,A, 'g', 'LineWidth', 2)
plot(t,A_derivative, 'r--', 'LineWidth', 2)
fplot(diff_test, [-2 10], 'bo', 'LineWidth', 2)
title('Signal A')
xlabel('Zeit "t"')
ylabel('a(t) und a_derivative(t)')
%% Signal B
subplot(4,1,2)
hold on, grid on, axis equal
% Beide Funktionen für Signal B funktionieren
b = @(t) heaviside(t-2) - heaviside(t-8) + heaviside(t-4) - heaviside(t-6);
% b = @(t) heaviside(t-2) - heaviside(t-4) + 2*(heaviside(t-4) - heaviside(t-6)) ...
% + heaviside(t-6) - heaviside(t-8);
B = b(t);
b_derivative = @(t) dirac(t-2) - dirac(t-8) + dirac(t-4) - dirac(t-6);
B_derivative = b_derivative(t);
plot(t,B, 'g', 'LineWidth', 2)
plot(t,B_derivative, 'r--', 'LineWidth', 2)
title('Signal B')
xlabel('Zeit "t"')
ylabel('b(t) und b_derivative(t)')
%% Signal C
subplot(4,1,3)
hold on, grid on, axis equal
c = @(t) -2*heaviside(t-1) + 2*heaviside(t-3) + (t-4).*heaviside(t-4) - (t-4).*heaviside(t-6);
C = c(t);
c_derivative = @(t) -2*dirac(t-1) + 2*dirac(t-3) + heaviside(t-4) - heaviside(t-6);
C_derivative = c_derivative(t);
plot(t,C, 'g', 'LineWidth', 2)
plot(t,C_derivative, 'r--', 'LineWidth', 2)
title('Signal C')
xlabel('Zeit "t"')
ylabel('b(t) und c_derivative(t)')
%% Signal D
subplot(4,1,4)
hold on, grid on, axis equal
% d = @(t) 2*t.*(heaviside(t+1) - heaviside(t-1)) + (3-t).*(heaviside(t-1) - heaviside(t-3));
d = @(t) (2*t).*heaviside(t+1) - (3*t-3).*heaviside(t-1) - (3-t).*heaviside(t-3);
D = d(t);
d_derivative = @(t) 2*heaviside(t+1) + (2*t).*dirac(t+1) - 3*heaviside(t-1) ...
+ heaviside(t-3);
D_derivative = d_derivative(t);
plot(t,D, 'g', 'LineWidth', 2)
plot(t, D_derivative, 'r--', 'LineWidth', 2)
xticks(start:1:ende)
title('Signal D')
xlabel('Zeit "t"')
ylabel('d(t) und d_derivative(t)')%% ÜA Karlsruhe
% 2
% 2.1
clc, clear, clf
set(0,'DefaultFigureWindowStyle','docked')
% Signal A
figure('Name', 'RT_Karlsruhe 2.1', 'NumberTitle', 'off')
subplot(4, 1, 1)
hold on, grid on, axis equal
start = -2;
ende = 10;
t = linspace(start,ende,5000);
a = @(t) (t-2).*(heaviside(t-2) - heaviside(t-4)) + (t-6).*(heaviside(t-4) - heaviside(t-6));
A = a(t);
a_derivative = @(t) heaviside(t-2) - 4*dirac(t-4) - heaviside(t-6);
A_derivative = a_derivative(t);
syms x
diff_test = diff((x-2).*(heaviside(x-2) - heaviside(x-4)) + (x-6).*(heaviside(x-4) - heaviside(x-6)));
% x = t;
%
% Diff_test = diff_test(x);
plot(t,A, 'g', 'LineWidth', 2)
plot(t,A_derivative, 'r--', 'LineWidth', 2)
fplot(diff_test, [-2 10], 'bo', 'LineWidth', 2)
title('Signal A')
xlabel('Zeit "t"')
ylabel('a(t) und a_derivative(t)')
%% Signal B
subplot(4,1,2)
hold on, grid on, axis equal
% Beide Funktionen für Signal B funktionieren
b = @(t) heaviside(t-2) - heaviside(t-8) + heaviside(t-4) - heaviside(t-6);
% b = @(t) heaviside(t-2) - heaviside(t-4) + 2*(heaviside(t-4) - heaviside(t-6)) ...
% + heaviside(t-6) - heaviside(t-8);
B = b(t);
b_derivative = @(t) dirac(t-2) - dirac(t-8) + dirac(t-4) - dirac(t-6);
B_derivative = b_derivative(t);
plot(t,B, 'g', 'LineWidth', 2)
plot(t,B_derivative, 'r--', 'LineWidth', 2)
title('Signal B')
xlabel('Zeit "t"')
ylabel('b(t) und b_derivative(t)')
%% Signal C
subplot(4,1,3)
hold on, grid on, axis equal
c = @(t) -2*heaviside(t-1) + 2*heaviside(t-3) + (t-4).*heaviside(t-4) - (t-4).*heaviside(t-6);
C = c(t);
c_derivative = @(t) -2*dirac(t-1) + 2*dirac(t-3) + heaviside(t-4) - heaviside(t-6);
C_derivative = c_derivative(t);
plot(t,C, 'g', 'LineWidth', 2)
plot(t,C_derivative, 'r--', 'LineWidth', 2)
title('Signal C')
xlabel('Zeit "t"')
ylabel('b(t) und c_derivative(t)')
%% Signal D
subplot(4,1,4)
hold on, grid on, axis equal
% d = @(t) 2*t.*(heaviside(t+1) - heaviside(t-1)) + (3-t).*(heaviside(t-1) - heaviside(t-3));
d = @(t) (2*t).*heaviside(t+1) - (3*t-3).*heaviside(t-1) - (3-t).*heaviside(t-3);
D = d(t);
d_derivative = @(t) 2*heaviside(t+1) + (2*t).*dirac(t+1) - 3*heaviside(t-1) ...
+ heaviside(t-3);
D_derivative = d_derivative(t);
plot(t,D, 'g', 'LineWidth', 2)
plot(t, D_derivative, 'r--', 'LineWidth', 2)
xticks(start:1:ende)
title('Signal D')
xlabel('Zeit "t"')
ylabel('d(t) und d_derivative(t)')

  댓글 수: 0

댓글을 달려면 로그인하십시오.

채택된 답변

Birdman
Birdman 6 Apr 2020
You may use Symbolic Toolbox and its beauties for this case :) Here is the code:
syms y1(t) y2(t) y3(t) y4(t)
y1(t)=piecewise(2<=t<=4,t-2,4<t<6,t-6,0);
Dy1(t)=diff(y1);
y2(t)=piecewise(2<=t<=4,2,4<t<6,3,6<=t<=8,1,0);
Dy2(t)=diff(y2);
y3(t)=piecewise(1<=t<=3,-2,4<=t<=6,t-4,0);
Dy3(t)=diff(y3);
y4(t)=piecewise(-1<=t<=1,2*t,1<=t<=3,-t+3,0);
Dy4(t)=diff(y4);
t=-2:0.001:9;
subplot(4,1,1);plot(t,y1(t),t,Dy1(t));
subplot(4,1,2);plot(t,y2(t),t,Dy2(t));
subplot(4,1,3);plot(t,y3(t),t,Dy3(t));
subplot(4,1,4);plot(t,y4(t),t,Dy4(t));
Observe the results and let me know if it works.

  댓글 수: 1

Jann B
Jann B 16 Apr 2020
Thank you for the quick response.
It's not quite perfect yet.
I think i need to figure out how to set the impulse of the dirac-funktion to 1 before plotting it.

댓글을 달려면 로그인하십시오.

추가 답변(0개)

태그

제품


릴리스

R2019a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by