Fourier Transform e^(-t)

Hi. Why in MATLAB, why do we have to add a Heaviside function when doing Fourier transforms? For example when doing a Fourier transform of something simple, e.g. e^(-t), I get an error.

.

%%Error code

syms x w X

f = exp(-x)

X=fourier(f, x, w)

ezplot(X)

.

To fix this I need to write f = exp(-x)*heaviside(x);

Why is this?

Answer 1

[Torsten]

Because your f is not integrable over IR, but only over IR+.

Or what is integral_{t=-oo}^{t=0} exp(-t) dt ?

Best wishes

Torsten.

[himesh]

Hi, Thanks for the answer.

Can you please explain what IR and IR+ is? Im not sure what you mean.

Thanks again

[Torsten]

I mean that

integral_{t=-oo}^{t=00} exp(-t) dt

does not exist, but only

integral_{t=0}^{t=oo} exp(-t) dt.

For the Fourier transform to exist, it would be necessary that

integral_{t=-oo}^{t=00} exp(-t) dt < oo

which is not the case.

Best wishes

Torsten.

[himesh]

Thanks. I also have one last question and that is when plotting these, I have to write

ezplot(abs(X))

Why are there errors when I get rid of the abs() in the ezplot statement?

Many thanks

Answer 2

[sarath sai krishna babu gunupudi]

Display the expression after computing Fourier Transform of u(t).

Save u(t) function in variable x and Fourier transform in variable xf.

Answer 3

[hategekimana shadrack]

Use matlab to calculate the Fourier series of the following periodic signals.

a. Draw the Amplitude spectrum of signal.