Fuzzy Methods in Nonlinear Signal Processing: Part II—Applications - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 90

FIGURE 3.16
(a) WD of three Gaussian atoms and the (b) a 7 9median, and (d) center affine

filter outputs. (From G.R. Arce and S.R. Hasan, IEEE Trans. Signal Process. , 48, 2321-2331, Aug.
2000. c

× 7median, (c) 9 ×

2000 IEEE. With permission.)

median filter, we apply each filter to the original WD. The results for the
7

9 median, and center affine filters are shown in Figure 3.16b
to d. As the figure shows, the result of applying a median filter to the WD
is not adequate because, although the cross terms are somewhat reduced,
significant distortion is introduced into the autoterm components. The center
affine filter, in contrast, significantly reduces the cross terms while preserving
the autoterms.
As a final practical example, consider the processing of protein sequence
data. 25 The amino acid sequence of protein may be considered as a 20-symbol
alphabet sequence, or it may be considered a sequence of numerical values
reflecting various physiochemical aspects of the amino acids, such as hy-
drophobicity, bulkiness, or electron-ion interaction potential (EIIP). 26 Analy-
sis of the numerical representation of sequences often identifies characteristic
patterns that may be too weak to be detected as patterns of symbols. 27 It has
been shown 27 , 28 that proteins of a given family have a common characteristic

× 7 median, 9 ×