Plane waves in three dimensions |

where the vertical axis is time; the horizontal axis is space; and the `` ''s are zeros. Another possibility is the 2-D whitening filter

Imagine all the coefficients vanished but and the given 1. Such filters would annihilate the appropriately sloping plane wave. Slopes that are not exact integers are also approximately extinguishable, because the adjustable filter coefficients can interpolate in time. Filters like (2) do the operation , which is a component of the gradient in the plane of the wavefront,

You might find it alarming that your teacher is not fully prepared to explain the difference between a volume and two planes, but please remember that we are talking about the factorization of the volumetric spectrum. Spectral matrices are well known to have structure, but books on theory typically handle them as simply . Anyway, wherever you see an in a three-dimensional context, you may wonder whether it should be interpreted as a cubic filter that takes one volume to another, or as two planar filters that take one volume to two volumes as shown in Figure 2.

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An inline 2-D PEF and a crossline 2-D PEF
both applied throughout the volume.
To find each filter,
minimize each output power independently.
Figure 2. | |
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Plane waves in three dimensions |

2013-07-27