Practical Signals Theory with MATLAB Applications, 2nd Edition

Appendix CThe Illustrated Laplace Transform

In the pages that follow, a series of Laplace transform pairs are presented, each showing a function of time on the left and the corresponding pole-zero diagram for on the right, where:

Each of the may be considered as the impulse response of a linear time-invariant (LTI) system. In each pole-zero diagram, poles are shown with a X while zeros are plotted with a O. The region of convergence shown shaded in each pole-zero diagram is generally the entire -plane to the right of the rightmost pole.

The inverse Laplace transform is only generally found from the pole-zero diagram of , as constant values or gain factors are not visible when poles and zeros are plotted. Similarly, the sum of two pole-zero diagrams is not generally the sum of the corresponding ...