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
2. A finite length signal has a discrete frequency domain
3. 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)
4. 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.

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
2. A finite length signal has a discrete frequency domain
3. 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)
4. A discrete-time signal has a finite frequency domain (again, this is a dual of 2, for the same reason).

* "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.