900
800
700
600
500
400
300
200
100
0
Magnitude of DFT
0
1 0
2 0
3 0
40
50
(a)
Frequency
84
Biomedical Signal and Image Processing
1
0.9
0.8
0.7
0.6
–10
–8
–6
–4
–2
0
2
4
6
8
1 0
g(t)
0.5
0.4
0.3
0.2
0.1
0
Time
FIGURE 5.6 Rectangular time window used for STFT.
For the shift values 3 ≤ a ≤ 7, the STFT will be zero as the shifted window captures a zero part of the signal that contains no time events. For a = 8 (Figure 5.7b),
the STFT captures the second event in the signal, i.e., the sinusoidal variations.
Again, for 10 ≤ a ≤ +∞, no event is captured by the STFT, and, therefore, no
particular information is in this part of the signal.
As can be seen in the previous example, the STFT seems to address the disadvantage of the FT being blind to the time localization. In reality, several different types of time windows are used for the STFT. These popular windows
include triangular windows as well as trapezoidal windows. Such windows, even
though distort the amplitude of the extracted portion of the signal, assign more
FIGURE 5.7 (a) Magnitude of STFT for a = 1.