Development of a wavelet-based algorithm to detect and determine ...
Development of a wavelet-based algorithm to detect and determine ...
Development of a wavelet-based algorithm to detect and determine ...
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6.2. BASIC IDEAS OF THE WAVELET TRANSFORM 47<br />
Calculation <strong>of</strong> the Continuous Wavelet Transform<br />
The calculation <strong>of</strong> the continuous <strong>wavelet</strong> transform is a quite simple process. There<br />
are five steps:<br />
1. Chose a <strong>wavelet</strong> <strong>and</strong> locate it at the start section <strong>of</strong> the original signal.<br />
Figure 6.9: Step 1 <strong>of</strong> the continuous <strong>wavelet</strong> transform<br />
2. Calculate a <strong>wavelet</strong> coefficient according <strong>to</strong> Equation 6.6.<br />
3. Shift the <strong>wavelet</strong> <strong>to</strong> the right <strong>and</strong> repeat step 1 <strong>and</strong> 2 until the whole signal is<br />
covered.<br />
Figure 6.10: Step 3 <strong>of</strong> the continuous <strong>wavelet</strong> trans-<br />
form<br />
4. Scale the <strong>wavelet</strong> <strong>and</strong> repeat step 1 through 3<br />
5. Repeat step 1 through 4 for all scales.<br />
With the help <strong>of</strong> the <strong>wavelet</strong> transform, a one-dimensional signal can be represented<br />
in two-dimensional domain. Figure 6.12 shows, as an example, the <strong>wavelet</strong> domain
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