Plotting a unit step function without heaviside.

So for my class I need to be able to plot

   Xg(t)= u(t+1)-2u(t-1)+u(t-3)
   Xh(t)=(t+1_u(t-1)-tu(t)-u(t-2)

and a whole other host of things but for these ones I'm confused on how to do it without the heaviside function. I got an answer for just u(t) was:

t = (-1:0.01:5)';
unitstep = t>=0;
plot(t,unitstep)

This worked.

When I tried to get it to shift instead the line became more of a ramp function.

t = (-1:0.01:5)';
unitstep = t>=0;
u1 = unitstep.*(t+1)
plot(t,u1)

What am I doing wrong?

[Ulfah Nizam]

what does 0.01 means in

t =(-1:0.01:5)';

[Adam Turton]

Matlab has an issue with jump discontinuities, so 0.01 makes it so that it "updates" the function to the correct placement, allowing what would otherwise plot as a ramp function to show as a near vertical line.

Answer 1

[Chad Greene]

Hi Hannah,

Your unitstep contains only zeros and ones. So when you plot

plot(t,unitstep)

it's a Heaviside function, just as you expect. But when you multiply unitstep by t, you end up plotting zeros wherever unitstep is zero, and the values of t (not ones!) wherever unitstep is one. If you're trying to move a simple Heaviside function left or right, try this:

t = (-1:0.01:5)'; 

% Start with all zeros: 
unitstep = zeros(size(t)); 

% But make everything corresponding to t>=1 one:
unitstep(t>=1) = 1; 

plot(t,unitstep,'b','linewidth',3) 

% Repeat, with everything shifted to the right by 1 unit: 
unitstep2 = zeros(size(t)); 
unitstep2(t>=2) = 1; 

hold on
plot(t,unitstep2,'r:','linewidth',2)
box off

[Hannah Chamberlain]

Thanks so much for the help! I'm not sure though how I would be able to shift this to the left though. I tried putting in negatives but it didn't give me what I wanted. Also, I need to add them together and get one result. Would this work? Using the earlier code too of course.

Xg= unitstep+unitstep2
plot(t,Xg)
axis([-2 5 0 1.5])

[Chad Greene]

Hannah, defining the unitstep function requires just two lines of code. Start with a vector of all zeros, then change them to ones wherever you want them to be one. In the example above, I said

 unitstep = zeros(size(t)); 
 unitstep(t>=1) = 1;

which made all values in unitstep one wherever t is greater than or equal to 1. To shift the location of the step, simply change the t>=1 argument to a different value. If you want to move the heaviside function to the left, you could say

 unitstep = zeros(size(t)); 
 unitstep(t>=-3) = 1;

which would place the step at -3. Does that make sense?

[Chad Greene]

Run this:

% Define some nominal unit step:
t = (-1:0.01:5)'; 
unitstep = zeros(size(t)); 
unitstep(t>=1) = 1; 

% Plot the unitstep twice: 
plot(t,unitstep,'k-','linewidth',2) 
axis([-2 5 0 1.5])
hold on
h = plot(t,unitstep,'b'); 

% Change the location of the unitstep:
for k = 0:30:1000

     % Create a new unitstep:
     newunitstep = zeros(size(t)); 
     newunitstep(t>=(1.5*sind(k)+1)) = 1; 

     % Update the blue line with the new unitstep:
     set(h,'ydata',newunitstep)

     % Pause 0.2 seconds so you can see it: 
     pause(0.2) 
end

[Hannah Chamberlain]

Thanks so much for the help. I think it wasn't working earlier because the value of t was too small. The only thing I still need to do is be able to add the functions together. So I need to do Xg(t)= u(t+1)-2u(t-1)+u(t-3). Here is my attempt. I don't think this is what it's suppose to look like.

t = (-2:0.01:5)'; 
% Start with all zeros: 
unitstep = zeros(size(t)); 
% But make everything corresponding to t>=1 one:
unitstep(t>=-1) = 1; 
%plot(t,unitstep,'b','linewidth',3) 
% Repeat, with everything shifted to the right by 1 unit: 
unitstep2 = zeros(size(t)); 
unitstep2(t>=1) = 1; 
%hold on
unitstep3 = zeros(size(t)); 
unitstep3(t>=3) = 1;
Ut= unitstep+unitstep2+unitstep3;
plot(t,Ut)
axis([-2 5 0 4])

[Chad Greene]

Perhaps you wanted to multiply the unitsteps together rather than add them?

Answer 2

[Les Beckham]

You are very close to the first half of your goal.

Your line of code

Ut= unitstep+unitstep2+unitstep3;

should, I believe, reflect what you are calling Xg in your original problem. You might want to rename it to help you remember the connection between the code and the original equation. Also, you need to look at what the multipliers/coefficients are in your original Xg definition. u(t-1), which you are calling unitstep2 in your code, is multiplied by -2 when assembling the total Xg. This is not reflected in your code.

I think you can figure it out from here.

[Hannah Chamberlain]

Thank you so much for you help!! It was enough that I was able to finish the rest of the assignment on my own.

[Les Beckham]

You are quite welcome.

Answer 3

[abdelkader omr]

I want to plot a unit step function

x axis represenets time and its value [0 1 2 3 4 5 6 7]

y axis represents load and its value are[2 2 3 3 3 3 2 2]

Answer 4

[Sam Chak]

Hi @abdelkader omr

Your function looks somewhat like a Boxcar function. However, your description of the continuous-time function is slightly unclear because they are discrete values. There are simpler methods for continuous-time, but since yours are discrete values, perhaps you may consider flexibly creating the function as follows:

%% Boxcar function
function y = boxcar(x, params)
    for i = 1:length(x)
        if     x(i) <= params(1)
            y(i) = 2;
        elseif x(i) <= params(2)
            y(i) = 2;
        elseif x(i) <= params(3)
            y(i) = 2;
        elseif x(i) <= params(4)
            y(i) = 3;
        elseif x(i) <= params(5)
            y(i) = 3;
        elseif x(i) <= params(6)
            y(i) = 3;
        elseif x(i) <= params(7)
            y(i) = 2;
        elseif x(i) <= params(8)
            y(i) = 2;
        else
            y(i) = 2;
        end
    end
end

%% Plot the function
x   = linspace(0, 10, 1001);
y   = boxcar(x, [0 1 2 3 4 5 6 7]);
plot(x, y, 'linewidth', 2), grid on, ylim([1 4])
xlabel('Time'), ylabel('Load'), title('Boxcar function')