Figure 3.5: Sorted wavelet coefficients for different basis functions in power framework.
The db9 basis produces the most sparse representation.
a wavelet basis and s is a sparse vector. Wavelet basis are very efficient in sparse
modeling of spatial correlation, as shown in Figure 3.4. The left side of the figure
images the variations of a chip in the spatial domain. The right side shows the
variations in the wavelet domain. In the wavelet domain most of the non-zero
coefficients are concentrated in the upper-left corner of the transform and most
of the remaining coefficients are close to zero.
Figure 3.5 shows wavelet transformation of variations for a number of wavelet
bases. The figure demonstrates the coefficients decay rate for a variety of wavelet
families on typical 32×32 regular grid circuits. The figure suggests that the
Daubechies 9 (db9) wavelet basis is very good at sparsifying the process variation.
In the remainder of the thesis, we use the Daubechies 9 wavelet to model process
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