Biomedical Engineering Reference
In-Depth Information
STFT (TIME VS. FREQUENCIES)
12
10
8
6
4
2
0
0
50
100
150
200
250
300
350
400
450
TIME (ms)
FIGURE 11.31 A two-dimensional rendering of the STFT of the aperiodic aortic pressure tracing shown in
Figure 11.2. The window size was matched as closely as possible to the heart rate. The mean was removed from
the signal so the variation in the lowest frequencies—that is, frequency level 0—reflects changes with respiration.
Haar Wavelet
Daubechies Wavelet
1
1
0.5
0.5
0
0
0.5
0.5
1
1
0
0.5
1
0
2
4
FIGURE 11.32 The general shape of two wavelets commonly used in wavelet analysis. The sharp corners
enable the transform to match up with local details not possible to observe when using a Fourier transform that
matches only sinusoidal shapes.
The notation for the 2D WT is
1
C ð a
,
s Þ¼
x ð t Þ'ð a
,
s
,
t Þ dt
ð
11
:
57
Þ
1
where a
the position factor. C can be interpreted as the correlation
coefficient between the scaled, shifted wavelet and the data. Figure 11.33 shows the db2
(
¼
scale factor and s
¼
j
(t)) wavelet at different scales and positions—for example,
j
(2,-100,t)
¼ j
(2t-100). The
inverse wavelet transform
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