Piecewise to Heaviside problem
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Hi all,
Trying to create a plot using heaviside function after being given a piecewise function. The code, I managed to get 2 different results, so I am not sure which is correct.
The piecewise function is the following:
x^2 - 1; if 0 <= x < 2
f(x) = 2x - 3; if 2 <= x < 5
sin(x); if x >= 5
My code is the following.
y = (t.^2-1).*[heaviside(t)-heaviside(t-2)]+(2.*t-3).*[heaviside(t-2)-heaviside(t-5)]+sin(t).*heaviside(t-5);
plot(t,y)
I may have made a mistake in the conversion to heaviside, and I am not so well versed in the step function, so it's a little challenging to analyze the graph to see whether or not it is correct. Any input is greatly appreciated!
Réponse acceptée
Ameer Hamza
le 26 Nov 2020
Yes, your code is correct. Following will work
t = 0:0.01:10;
y = (t.^2-1).*[heaviside(t)-heaviside(t-2)]+(2.*t-3).*[heaviside(t-2)-heaviside(t-5)]+sin(t).*heaviside(t-5);
plot(t,y)
However, an easier solution is to use piecewise()
syms x
f(x) = piecewise(0<=x<2, x^2-1, 2<=x<5, 2*x-3, 5<=x, sin(x));
fplot(f, [0 10])
Plus de réponses (1)
Walter Roberson
le 26 Nov 2020
syms f(x) t
f(x) = piecewise(x<0, 0, 0 <= x & x < 2, x^2 - 1, 2 <= x & x < 5, 2*x - 3, 5 <= x, sin(x));
f(t)
sympref('HeavisideAtOrigin', 1);
y = (t.^2-1).*[heaviside(t)-heaviside(t-2)]+(2.*t-3).*[heaviside(t-2)-heaviside(t-5)]+sin(t).*heaviside(t-5)
yp = rewrite(y, 'piecewise')
fplot(f(t)-y, [-1 10])
The formulas come out the same except in a different order of cases, and the difference between the two appears to be all zero
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