Problem trying to integrate a function

function rect = t1(x)
if   x < 1 && x > -1
    rect = 1;
else
    rect = 0;
end

this was my function in a separate script file.

syms e x
pattern1 = t1(x);
ftpattern1 = int(pattern1*exp(-2*i*pi*e*x),x,-inf,inf);

Matlab keeps on giving a message that says I have an error in t1 if x < 1 && x > -1. I think I'm not allowed to give logical expression to symbols such as x... Any suggestions?

Answer 1

[Star Strider]

You’re close, but you’re not defining it correctly.

The definition of a pulse in the Symbolic Math context:

syms x w t T
rect = heaviside(x+1) - heaviside(x-1);

figure(1)
ezplot(rect, [-2 2])                    % Display Function
grid

However the correct way to define it in terms of calculating its Fourier transform is to define it as 1 between -T and +T:

syms x w t T

ftpattern1 = int(1*exp(-j*w*t), t, -T, T)

produces:

ftpattern1 =

(2*sin(T*w))/w

Here, you can define T=1, and plotting it:

ftpattern1 = subs(ftpattern1, T, 1)

figure(2)
ezplot(ftpattern1, [-10*pi, 10*pi])
grid

This is the expected result.