Defining Dirac Function matlab

x(t) = t(u(t + 2) − 3 u(t − 3) + 2 u(t − 5))

How can I plot this function, with u as the diriac and t as a variable?

[Walter Roberson]

It seems much more likely to me that you want Heaviside rather dirac.

[Rik]

I agree with Walter. If so, you could implement the Heaviside function (if there is not already an implementation built in) with something like (x+abs(x))/2

Answer 1

[Walter Roberson]

heaviside exists in the Symbolic Math toolbox. Please be careful about the value of heavside(0); since R2015a you have been able to configure that value using sympref()

dirac exists in the Symbolic Math toolbox as well. Please remember that dirac() is technically a distribution, and that dirac(x) is 0 for all non-0 x and is infinite for x == 0, so multiplying dirac(x) by a constant only makes sense if you are integrating a function that contains dirac() (in which case you get the heaviside step function.)

Answer 2

[Carlos M. Velez S.]

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