Piecewise to Heaviside problem

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!

[xRah]

I included the code that I assumed to be correct

Answer 1

[Ameer Hamza]

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])

[xRah]

It seems that using the piecewise route shows the same graph as mine. I forgot to include the values of t in the code above. Thank you Hamza for the clarification. I really do appreciate it!

Answer 2

[Walter Roberson]

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)

ans = 

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)

y = 

yp = rewrite(y, 'piecewise')

yp = 

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

[xRah]

Hi Walter and thank you for your input.

I am not entirely sure I follow everything you did, but how come your output graph looks different from my output?