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 48<br />
Figure 6.11: Step 4 <strong>of</strong> the continuous <strong>wavelet</strong> trans-<br />
form<br />
Figure 6.12: The continuous <strong>wavelet</strong> transform (Here:<br />
f=800/a, t=b)<br />
representations <strong>of</strong> a power signal. figure 6.12(a) displays the signal which contains 3rd<br />
harmonic component. The signal is transferred in<strong>to</strong> 32 scales through Morlet <strong>wavelet</strong>,<br />
where the relation between scale <strong>and</strong> frequency is: frequency = 800/scale. Figure<br />
6.12(b) displays the <strong>wavelet</strong> representation on the time-scale plane in 2D, where the<br />
dark degree is proportional <strong>to</strong> the absolute value <strong>of</strong> the <strong>wavelet</strong> coefficients. It can be<br />
seen that the <strong>wavelet</strong> transform locates the energy around scale 16 <strong>and</strong> 5.34 (i.e. 50 Hz<br />
<strong>and</strong> 150 Hz), which corresponds <strong>to</strong> the fundamental frequency <strong>and</strong> the 3rd harmonics<br />
in the signal, <strong>and</strong> shows the time information <strong>of</strong> the signal at the same time. Creating<br />
the <strong>wavelet</strong> coefficients at every possible scale leads <strong>to</strong> a large quantity <strong>of</strong> the calcula-<br />
tion because the continuous <strong>wavelet</strong> transform is great redundant. Because the basic<br />
calculation <strong>of</strong> the CWT is an inner product or a convolution, there are some faster algo-
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