Mechanical interpretation

Because of the stringent conditions on minimum-phase wavelets, you might wonder whether they can exist in nature. A simple mechanical example should convince you that minimum-phase wavelets are plentiful: denote the stress (pressure) in a material by x_t, and denote the strain (volume change) by y_t. Physically, we can specify either the stress or the strain, and nature gives us the other. So obviously the stress in a material may be expressed as a linear combination of present and past strains. Likewise, the strain may be deduced from present and past stresses. Mathematically, this means that the filter that relates stress to strain and vice versa has all poles and zeros outside the unit circle. Of the minimum-phase filters that model the physical world, many conserve energy too. Such filters are called ``impedances'' and are described further in FGDP and IEI, especially IEI.