Two-dimensional Digital Filters by Wu-Sheng Lu

By Wu-Sheng Lu

Offers uncomplicated theories, suggestions, and approaches used to research, layout, and enforce two-dimensional filters; and surveys a couple of purposes in photo and seismic info processing that reveal their use in real-world sign processing. For graduate scholars in electric and laptop e

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And sinusoid. 11) and has a finite support S = (0, 0). 12) and has a support S = {(nl, n2) : n, 2 0 and n2 z 0). The unit impulse and unit step are illustrated in the discrete contour maps of Fig. 6 Signal flow-graph representation of 2-D digital filters. b where each dot represents a signal value of unity. The more important of these two fundamental signalsis the unit impulse since it can be used to synthesize any other 2-D discrete signal, or conversely, any 2-D signal can be decomposed into impulses, as will be demonstrated below.

Some more advanced methods for space-domain analysis will be examined in Chapter 2. 10 A k , X k2 rectangular unit pulse. 2 (a) Find the impulseresponse of the filter described in Fig. 5a. (b) Find the impulse response of the filter characterized by the equation Y ( h n2) = 4 4 , n2) + bY(4 - 1, n2 - 1) Assume that the filter is initially relaxed, that is, y(n,, n2) = 0 for n, < 0 or n2 < 0 Solution. (a) With x(n,, n2) = 6(n,, n2), Eq. 9) becomes v(n,, n2) = 6(n,, n2) + ealv(nl - 1, nz) If n2 = 0, then v(0, 0) v(1, 0) 4 2 , 0) 1 + ea%(- 1, 0) = 1 = 0 + ealu(O, 0) = eal = 0 + ealv(l, 0) = eZa1 = ...

L . l l d , and is then shifted in the positive directions of The values in Fig. 11~ are then the two axes, as illustrated in Fig. 11~. multiplied by the corresponding values in Fig. l . l l a t o form Fig. lle. The sum of all the products in Fig. l . l l e gives the response of the filter for nl and n,, as illustrated in Fig. llf. 7 STABILITY A 2-D digital filter is said to be stable in the bounded-input, bounded- output (BIBO) sense, if a bounded input such that Ix(nl, n,)l S M < for all n, and n, and some M yields a bounded output, that is, ly(n,, n,)l S N

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