How to plot this function with 2 variables?

Hello, I’m having a hard time plotting z2(t). I keep getting the error “input must be a function or functions of a single variable”. I’m not sure how to properly define “u”.

[Marisa]

[Dyuman Joshi]

As you are using fplot, the expected input is a function handle.

And the syntax to define a function handle is

name_of_handle = @(independent_variables) relation_or_expression_of_independent_variables

%For the first example, it translates to 
z1 = @(t) exp(t);

Refer to these links for more information -

https://in.mathworks.com/help/matlab/ref/function_handle.html

https://in.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html

Answer 1

[Voss]

t = -2:0.01:2;

z1 = exp(t);
z2 = 2*(t+1 >= 0);
z3 = 0.5*sin(7*t);

hold on
grid on

plot(t,z1,'-','LineWidth',2)
plot(t,z2,':','LineWidth',2)
plot(t,z3,'--','LineWidth',2)

xlabel('t')
ylabel('z')
legend("z"+[1 2 3])
ylim([-1 8])

[Dyuman Joshi]

Just a note -

z2 = 2*(t+1 >= 0);

">= 0" is not mentioned in the question

[Voss]

I interpret u(t) to be the unit step function.

[Dyuman Joshi]

Alright.

[Marisa]

Thank you, The original question wants me to plot z2(t)=2u(t+1), I’m not sure how to plot this since it also involves “u”

[Sam Chak]

The signal u(·) in the question most likely refers to the unit step function, which can be represented by the Heaviside function.

https://www.mathworks.com/help/symbolic/heaviside.html#description

t  = -2:0.001:2;
z2 = 2*heaviside(t + 1);
plot(t,z2,':','LineWidth',2), grid on
xlabel('t')
ylabel('z')
ylim([-1 8])

[Marisa]

Okay the example mentioned Heaviside but I tried to use that and wasn’t getting it right. This makes sense! This worked, thank you so much! I was just putting Heaviside in incorrectly.

[Voss]

@Marisa: Or if you don't have the Symbolic Math Toolbox, you can write down what the unit step function is in your definition of z2, as I have done in my answer.

[Sam Chak]

Good to hear that, @Marisa. 👍

[Sam Chak]

Hi @Marisa

In the mathematical representation of linear physical systems (later in your course), you may encounter the state-space equation, . But this is not the unit step function. Please keep that in mind.