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3.5 Pyramids and wavelets 129

(a) (b)

(c) (d)

Figure 3.28 Two-dimensional image interpolation: (a) bilinear; (b) bicubic (a = −1); (c) bicubic (a = −0.5);
(d) windowed sinc (nine taps).

1.0
windowed-sinc 0
tent -0.5 0.0 windowed-sinc 0.5
cubic a=-0.5 -20 cubic a=-0.5
cubic a=-1 tent
-40
cubic a=-1
0.5 -60
-80
-100
-120
0.0
-4 -3 -2 -1 0 1 2 3 4 -140
-160
-180
-0.5 -200
(a) (b)

Figure 3.29 (a) Some windowed sinc functions and (b) their log Fourier transforms: raised-cosine windowed
sinc in blue, cubic interpolators (a = −1 and a = −0.5) in green and purple, and tent function in brown. They
are often used to perform high-accuracy low-pass filtering operations.