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