Plotting the derivative of an "switch-funktion"

1 回表示 (過去 30 日間)
Jann B
Jann B 2020 年 4 月 6 日
コメント済み: Jann B 2020 年 4 月 16 日
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)')

採用された回答

Birdman
Birdman 2020 年 4 月 6 日
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.
  1 件のコメント
Jann B
Jann B 2020 年 4 月 16 日
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.

サインインしてコメントする。

その他の回答 (0 件)

カテゴリ

Help Center および File ExchangeFourier Analysis and Filtering についてさらに検索

タグ

製品


リリース

R2019a

Community Treasure Hunt

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

Start Hunting!

Translated by