The term translation is related to the location of the window, as
the window is shifted through the signal. This corresponds to the
time information in the transform domain. But instead of a frequency
parameter, we have a scale. Scaling, as a mathematical
operation, either dilates or compresses a signal. Smaller scales correspond
to dilated (or stretched out) signals and large scales correspond
to compressed signals.
The wavelet series is simply a sampled version of the CWT, and
the information it provides is highly redundant as far as the reconstruction
of the signal is concerned. This redundancy, on the other
hand, requires a significant amount of computation time and
resources.
The multilevel 1D wavelet decomposition function, available in
Matlab is chosen with the Morlet wavelets specified. It returns the
wavelet coefficients of signal X at scale N (Soman & Ramachandran,
2005). Fig. 6 shows Morlet wavelet.
Sixty four scales are initially chosen to extract the Morlet wavelet
coefficients of the signal data. The efficiency of sixty four scales
of Morlet wavelets were obtained using WEKA data mining software
and the coefficients of highest scale are considered for classification.
Since the eighth scale gave maximum efficiency of 96.5%,
the statistical features corresponding to it were given as input for
J48 algorithm to determine the predominant features to be given as an input for training and classification using SVM. Fig. 7 gives
the efficiencies of all scales.