Algorithms and Parallel Computing

13.4 3-D DIGITAL FILTERS

A first-quadrant 3-D recursive filter can be represented by the equation

(13.15)

where X ≡ X (z₁, z₂, z₃), Y ≡ Y (z₁, z₂, z₃), and b(0, 0, 0) = 0. In the above equation, h is the height of the filter window, w is the width of the filter window, and f is the depth of the filter window, which is the number of frames used to collect the filter input samples.

Assuming progressive raster-scanned data, the term represents one time-step delay through the use of a single register as a storage element. The term represents W time-step delays where W is the frame width. The term represents HW time-step delays where H is the frame height. These delays could be implemented as memory address locators for use by the software threads, or they could be implemented as actual hardware buffers for use by the software systolic array processing elements.

The above equation can be written in a hierarchical way as

(13.16)

where the terms F₂(k₃) and G₂(k₃) are two 2-D IIR filter ...