Windowed fft: how windowing is practically applied at overall data?

Hi, please, somebody tell me: how windowing is practically applied at overall data?

Suppose I simply have T = 1000 original samples and a window W = 200 points, of Hanning type. I study, therefore, the simplest case without the overlappings of windows between the end and the beginning of each segment and, obviously, the window weights have already been calculated, ...

PROCEDURES (I am looking for basics, although Matalab could have its particolar functions)

1)I divide the T = 1000 original data samples into 5 segments of width W = 200 samples each.

2)Then I apply the W = 200 Hanning window to each of the 5 (=1000/200) portions of the original signal.

3)Thus, I join/add these 5 portions of windowed signal. In the end, I obtain the T = 1000 original samples of the signal, to which the right windowing was applied.

All these steps without calculating any fft.

4)Finally, I calculate the "global" vector fft(T = 1000 original samples with windowing, 1000).

Obviously number T = 1000, can also be understood as the addition of zeropadding samples at the end.

Is the procedure correct?

Greetings, Michele Di Savino

P.S. Else, I could call 5 fft(200 original samples with windowing, W = 200), but certainly the 5 vectors fft() obtained them cannot be join naked: you should see the fft mathematics.