Effect on the Limit Curve

Each of the a1 factors in the mask multiplies the amplitudes of the signal and artifact components by these factors. 

Primal schemes have an even number of a factors in the mask, and so all that is left is the kernel of the scheme. 

The kernel by definition has no further factors of a, but it can be expressed as a polynomial in a. In fact, because the kernel of a binary scheme always has an odd number of entries, its symmetric form can be expressed as a polynomial in a2. 

Each term in that polynomial multiplies the signal and artifact by an appropriate power of cos2(ttlu/2) or sin2(irw/2) respectively, and the resulting contributions can be added together again. 

We thus see that the effect of one step of the complete scheme is computed by expressing the mask as a polynomial in a2, and then evaluating that polynomial as a function of cos2(i uj/2) for the signal and sm2(7rw/2) for the artifact. 

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