signal fourier transform include unit step function

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hey there
hey there 2020-7-1
评论： Star Strider 2021-1-25
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

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Star Strider
Star Strider 2020-7-1
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.
.
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