By Der-Tsai Lee, Majid Sarrafzadeh

Discussing algorithmic facets of VLSI format, this article contains insurance of: matters in timing pushed structure; LP formula of worldwide routeing and location; Stockmeyer's floorplan optimization strategy; the ny and knock-knee routeing modes; and parallel algorithms for placement

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27, n)> = 2 E r = - o c M " - 2*0 < / ( « ) , ^a-i (« - 2-'fc) > +2 E r = - o c 9(n - 2fc) < / ( « ) , V2-J (« " 2-J'A:) > . 32) Algorithm Views of Discrete Wavelet Transform D2,(f)(n) —r> f2 — • 9(n)- —i i -i i i i K(f)(n) f2 — • h(n)- i{*>A°(f)(n) —L> L 1 Level IDWT 23 1 1 1 Fig. 6 The scheme to reconstruct signal at resolution 2 J + 1 from approximated signal at resolution 2 J and detail signal at resolution 2 J . This scheme is 1 level inverse DWT (IDWT). Finally, from Eq.

3, given a complementary set (h, g), any filter gnew that makes (h,gnew) complementary must be able to be obtained by applying a lifting step on g. 5, and the results are in Eq. 59. 3 further shows that g must be able to be obtained from g° by a lifting step. Finally, the lifting factorization algorithm can be derived. 2 -x^z)—r Original _ signal X(z) -si(z) »A2 ,> -ti(z) '' -sm(z) -tm(z) t1 >' •Xo(z)- (a) The forward DWT scheme using lifting facto Low-pass signal XL(Z)- 1/K High-pass XH(z) . signal K + ' Wz) sm(z) '' Wz) " +I '' •*' i I t2 sm(z) J I t2 (b) The Inverse DWT scheme using lifting facto Fig.

It can be directly derived from Eqs. 66. (2) (9, 7) filter 40 VLSI Design of Wavelet Low-pass signal High-pass signal X(2/c) DWT Transform X(2k) X(2*+1) Low-pass signal High-pass signal Mk) XH(A) IDWT Fig. 18 The haar wavelet scheme of DWT and IDWT based on lifting factorization. The (9,7) filter is a popular filter that has been adopted in JPEG 2000 standard for lossy image compression. The analysis filter h has 9 coefficients while the synthesis filter h has 7 coefficients for smoother scaling function.