""250 200 150 100 50 0 50 100 150 200 250

Figure 3.9. Biplot of first two score vectors (ti and t2, respectively) of the MPCA model representing normal operation with 95 and 99 % control limits.

is used to ensure that the energy of the scaled and translated signals are the same as the mother wavelet. Scale parameter specifies the location in frequency domain and translation parameter determines the location in time domain. This equation can be interpreted as the inner product of x(t) with the scaled and translated versions of the basis function [116]:

Scaled and translated versions of the basis functions are obtained from the mother wavelet (Eq. 3.27). The discrete wavelet transform is used to reduce the computational burden without losing significant information. To obtain the discretized wavelet transform, scale and translation parameters are discretized as a = V and b — 2J x k. Then, there exists with good time-frequency localization properties such that the discretized wavelets

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