# Dictionary:Fig Z-3

FIG. Z-3. z-plane. (a) The wavelet (10, -2, -1, 2 1) has the z-transform ${\displaystyle 10-2z-z^{2}+2z^{3}+z^{4}}$, which may be factored ${\displaystyle (2+j+z)(2-j+z)(-1-j+z)(-1+j+z)}$, which has the roots ${\displaystyle (-2-j)}$, ${\displaystyle (-2+j)}$, ${\displaystyle (1-j)}$, ${\displaystyle (1+j)}$. (b) A plot of these roots in the z-plane is shown. Since all roots lie outside a circle of radius 1 (the unit circle), the wavelet is minimum phase.