Aperiodic signals fourier transform short question?

Question

What is the fourier transform of the aperiodic signals with infinite sequence? How about the transform of aperiodic fourier signals with finite sequence?

Answer 1

While I'm not really sure what kind of answer you are looking for, I'll try:

I'll assume we are talking about continuous signals. The fourier transform of an aperiodic continuous signal is a way to represent the signal as a weighted integral of complex exponentials. The transform is defined as:

$$\hat{f}(\omega)=\int_{-\infty}^\infty f(t)e^{-j{\omega}t} dt$$

Where $f(t)$ is the original signal, ${\omega}$ is the angular frequency, ${t}$ is time. This is valid for both finite and infinite sequences. (For finite sequences, the integral can be cropped to the signal's span.)

Basically the transform is a domain change - the original signal is a function in time domain returning the signal's value at a given time, while its fourier transform is a function in frequency domain returning the amount of given angular frequency in the signal.

If this is not what you are looking for, please further define your question.