Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition

(42)

The DWT coefficient $c_{m,n}$ is given by

$c_{m,n}={\int }_{-\infty }^{+\infty }{{x(t)\mathrm{\Psi }}^{*}}_{m,n}(t)dt$ (43)

(43)

Here wavelets are orthonormal functions obtained by shifting and dilating a mother wavelet $\psi (t)$

${\mathrm{\Psi }}_{m,n}(t)=2^{-m/2}\mathrm{\Psi }(2^{-m}t-n)$ (44)

(44)

As $m$ increases, the wavelets stretch ...