In this chapter we will examine

- phase shift, analytic signal, and Hilbert transform.
- spectral factorization, i.e., finding a minimum-phase wavelet to fit any spectrum.
- a ``cookbook'' for Butterworth causal bandpass filters.
- phase delay, group delay, and beating.
- where the name ``minimum phase'' came from.
- what minimum phase implies for energy delay.

- HILBERT TRANSFORM
- SPECTRAL FACTORIZATION
- A BUTTERWORTH-FILTER COOKBOOK
- PHASE DELAY AND GROUP DELAY
- PHASE OF A MINIMUM-PHASE FILTER
- ROBINSON'S ENERGY-DELAY THEOREM
- FILTERS IN PARALLEL

Stanford Exploration Project

10/21/1998