> Fourier transform can be used to analyze the frequency domain of a specific period of signal. However, I saw many of these transforms in textbooks are based on entire signal sequences,

There are four closely related Fourier transforms.

1. An infinite length signal has a continuous frequency domain
1. A finite length signal has a discrete frequency domain
1. A continuous-time signal has an infinite frequency domain (this is a dual of 1, because the inverse Fourier transform is just a slightly modified Fourier transform)
1. A discrete-time signal has a finite frequency domain (again, this is a dual of 2, for the same reason).

```
|   time      |  length  | frequency        |  length  | name |
|-------------|----------|------------------|----------|------|
| continuous  | infinite |   continuous     | infinite | Fourier Transform* |
| continuous  |  finite  |    discrete      | infinite | Fourier Series |
| discrete    | infinite |   continuous     |  finite  | Discrete-time Fourier transform |
| discrete    |  finite  |    discrete      |  finite  | Discrete Fourier Transform** |
```
\* "Plain old" Fourier transform

\*\* AKA "DFT", it's what can be made fast for the FFT

Your confusion probably arises because the DFT/FFT is heavily used in signal processing algorithms, which are realized in hardware.  At the same time, the first three transforms in the table above are used strictly for _analysis_ -- analysis, in turn, is used heavily in designing digital signal processing algorithms.

So you'll see "the Fourier transform" mentioned, but there's _four flavors_.  In signal processing, the one that's actually used in algorithms is the FFT, because it's the only one that makes sense with sampled, finite-length data.