How to find the Fourier transform X(ω)

Hello world!

I want to find the fourier transform X(ω) of these continuous signals x(t).

Also I want to find the inverse fourier transform of these signal X(ω).

In addition, for each of the above questions, draw the signals x(t) and the spectrums Χ(ω) respectively.

I run this code for first questions but it doesn't work. Can anyone help me?

t =(-1:0.01:1)';
u == unitstep = t>=0;
x = (t.*exp(-3*t)*sin(8*t))*u;
f = fourier(x);
plot(f)

Answer 1

[Ameer Hamza]

fourier() works with symbolic inputs

syms t

x(t) = (t*exp(-3*t)*sin(8*t))*heaviside(t);
fourier(x)

[RoBoTBoY]

And how to plot this fourier transform? in order to plot I will need values for t.

[Ameer Hamza]

Fourier series itself return complex numbers. You need to plot its magnitude

syms t

x(t) = (t*exp(-3*t)*sin(8*t))*heaviside(t);
f = abs(fourier(x));
fplot(f, [0 10])

[RoBoTBoY]

In order to find the angle. will i use this?

f = angle(fourier(x));

[Ameer Hamza]

Yes. That is correct.

[RoBoTBoY]

How to perform the second question with code?