We present in Fig. 15 a comparison of the error kernel for several synthesis functions of same support W = 4. It includes cubic B-spline, cubic o-Moms, and cubic Schaum as examples of polynomial functions, and Dirichlet and Hanning as examples of apodized sinc.

FIGURE 16 Theoretical performance index for a first-order Markov model with p = 0,9. Triangles: Interpolating functions. Circles: noninterpolating functions.

We observe that the sinc-based synthesis functions do not reproduce the constant. Since most of the energy of virtually any image is concentrated at low frequencies, it is easy to predict that these functions will perform poorly when compared to polynomial-based synthesis functions. We shall see in the experimental section that this prediction is fulfilled; for now, we limit our analysis to that of the more promising polynomial cases.

On the grounds of Eq. (9), we can select a specific function/ to sample and interpolate, and we can predict the amount of resulting squared interpolation error. As a convenient simplification, we now assume that this function / has a constant-value power spectrum; in this case, it is trivial to obtain the interpolation error by integrating the curves in Fig. 15. Table 1 gives the resulting values as a signal-to-noise ratio expressed in decibels, where the integration has been performed numerically over the domain me [— n, n]. These results have been obtained by giving the same democratic weight to all frequencies up to Nyquist's rate; if low frequencies are considered more important than high frequencies, then the order of approximation L and its associated constant Cv are the most representative quality indexes.

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