Digital Signal Processing Reference
In-Depth Information
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Sample number
FIGURE 13.18
Four-subband compression for 32-bit seismic data and SNR ¼ 36 dB.
CWT, which will lay out the foundation. Next, we emphasize the DWT for applications of signal
coding.
Let us examine a signal sampled at 1 kHz with 1024
32 (32,678) samples given by
xðtÞ¼
0
:
5cos
ð
2
p
80
tÞ½uðtÞuðt
8
Þ þ
sin
ð
2
p
180
tÞ½uðt
8
Þuðt
16
Þ
þ
sin
ð
2
p
250
tÞ½uðt
16
Þuðt
32
Þ þ
0
:
1sin
ð
2
p
0
:
8
tÞ½uðt
8
Þuðt
24
Þ
(13.30)
The signal contains four sinusoids: 80 Hz for 0
t <
8 seconds, 180 Hz for 8
t <
16 seconds,
350 Hz for 16
t
32 seconds, and finally 0.8 Hz for 8
t
24 seconds. All the signals are plotted
separately in
Figure 13.19
while
Figure 13.20
shows the combined signal and its DFT spectrum.
Based on the traditional spectral analysis shown in
Figure 13.20
,
we can identify the frequency
components of 80, 180, and 350 Hz. However, the 0.8-Hz component and transient behaviors such as
the start and stop time instants of the sinusoids (discontinuity) cannot be observed from the spectrum.
Figure 13.21
depicts the wavelet transform of the same signal. The horizontal axis is time in seconds
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