     Next: Two poles Up: LEAKY INTEGRATION Previous: LEAKY INTEGRATION

## Plots

A pole is a place in the complex plane where a filter B(Zp) becomes infinity. This occurs where a denominator vanishes. For example, in equation (8) we see that there is one pole and it is located at .In plots like Figure 1, a pole location is denoted by a p'' and a zero location by a z." I chose to display the pole and zero locations in the -plane instead of in the Z0-plane. Thus real frequencies run along the horizontal axis instead of around the circle of |Z|=1. I further chose to superpose the complex -plane on the graph of versus .This enables us to correlate the pole and zero locations to the spectrum. I plotted in order that the and axes would coincide. As we will see later, some poles give stable filters and some poles give unstable filters. At the risk of some confusion, I introduced the minus sign to put the stable poles atop the positive spectrum. Since we will never see a negative spectrum and we will rarely see an unstable pole, this economizes on paper (or maximizes resolution for a fixed amount of paper).

In Figure 1, moving the p'' down toward the horizontal axis would cause a slower time decay and a sharper frequency function.     Next: Two poles Up: LEAKY INTEGRATION Previous: LEAKY INTEGRATION
Stanford Exploration Project
10/21/1998