How to plot delta dirac and unit step functions

Hey all, I am having trouble trying to plot (via stem) some delta dirac and unit step functions for my Digital Signal Processing class!

The ones in particular I am trying to plot are as follows:

Thanks!

[Walter Roberson]

What function did you find to implement dirac delta?

What function did you find to implement unit step function?

[Steven Artzer]

I'm sorry, what do you mean?

[Walter Roberson]

What have you accomplished so far? What particular parts are you looking for assistance with?

[Steven Artzer]

Sorry, I just don't know the syntax to plot those functions. Trying to get plots like this

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/stem.html

[Steven Artzer]

That still doesn't help me with the syntax of the functions I posted. It's not stem I need help with, but just the delta dirac and unit step syntax

[Walter Roberson]

DIRAC = @whatever_dirac_delta_function_you_find;
UNITSTEP = @whatever_unit_step_function_you_find;
t = linspace(-50, 50, 500);
Example3 = UNITSTEP(3-T);
stem(t, Example3);

That shows you the syntax . Now you have to find or write a function that implements dirac delta, and find or write a function that implements unit step function.

[Steven Artzer]

Okay then I guess I'm mostly trying to figure out how to plot the functions listed... Like how exactly I find or write a function in Matlab for those.

[Walter Roberson]

I already showed you how to plot the functions. What I posted above was actual code.

Further example of plotting.

t = 1 : 10;
y = randi([0 1], 1, 10);
stem(t, y);

I think you should concentrate on writing functions that implement dirac delta and unit step.

Answer 1

[Idin Motedayen-Aval]

This question is old, and the comments contain good hints on how to solve it, but I thought it might be instructive to put the code that solves this specific problem.

The code below shows a possible implementation of dirac and unit step functions, and uses them to plot the two functions given.

(The functions dirac and heaviside are from Symbolic Math Toolbox, and will require careful treatment to be used in this context, so I'm not using them below.)

n = -4:1:4;
fn1 = myDirac(n)+2.*myDirac(n-1);
fn2 = (4-n).*myUnit(n).*myUnit(3-n);
stem(n, fn1);
figure
stem(n, fn2);

function y = myDirac(x)
% return 1 only in places where x is zero
% return zero everywhere else
y = zeros(size(x));
y(x==0)=1;
end

function y = myUnit(x)
% return zero for x values less than 0
% return 1 for x >= 0
y = zeros(size(x));
y(x>=0) = 1;
end

Answer 2

[Kiran Felix Robert]

Hi Steven,

The Examples shown above can be used to plot the functions using stem.

Refer the documentation of Dirac-delta(Dirac)and unit-step(heaviside) they point to the MATLAB Built-in functions for the unit-step and Dirac-Delta Functions. You can use these Built-in functions to write your required expression and plot using stem.

Kiran Felix Robert

Answer 3

[Carlos M. Velez S.]

The examples above refer to the Kronecker delta function for discrete signals. If you want to apply the Dirac delta function in simulation to continuous-time systems, the following code is enough:

function y = delta_dirac(u)
[n,m] = size(u);
if max(n,m) ==1
    dt = 1e-6; % Define a small time increment for the delta function
else
    dt = u(2) - u(1);
end
y = zeros(n,m);
for i=1:max(m,n)
    if u(i) == 0
        y(i) = 1/dt;
    else
        y(i) = 0;
    end
end