signal fourier transform include unit step function

hey there. the question is this : x(t) = (exp(1)^-t)×u(t) note: u(t) is unit step function that has valeu 1 for (t >= 0) question is calcutlating X(w) the main idea is that (t) is symbol but u(t) only changes the range of fourier integral.

my code :

syms t;
t = linspace(-20, 20, 5000);
u = @(t) (t >= 0);
x = @(t) exp(1).^(-t).*u(t);
x_w = fourier(x(t))

error : check for missing argument or incorrect argument data type in call to function 'fourier'

i found that I can't handle that unit step function in x(t). when i don't have u(t) so I don't need t = linspace...... then every thing works great. but i need to solve this question

Answer 1

[Star Strider]

Try this version of your code:

syms t x(t) 
% t = linspace(-20, 20, 5000);
% u = @(t) (t >= 0); 
x(t) = exp(-t) * heaviside(t); 
x_w = fourier(x(t))

producing:

x_w =
1/(1 + w*1i)

The parts I commented (%) are not necessary here.

.

[hey there]

good job!

is this format correct too?

syms t
x = @(t) exp(-t) * heaviside(t); 
x_w = fourier(x(t))

[Star Strider]

Thank you!

Yes. When I ran it, the result was:

x_w =
1/(1 + w*1i)

This slightlly surprised me, because I did not believe that the Symbolic Math Toolbox recognised anonymous functions.

[ketul Modi]

what is @(t) here??

[Star Strider]

What Is a Function Handle?