## Cost

Let us assume that we want to compute the interpolated value fi(x) of an image fi at argument x, using a separable synthesis function of finite-support W. For each output value, we first need to perform W multiplications and W additions to compute q2 = ^ ckt,k2X1 — k1), with an inner loop over k1. This computation is embedded in a similar outer loop over k2 that is executed W times and that involves the computation of fi (x) = Ck2 f(x2 — k2). Finally, we need W2 mult-and-adds in two dimensions; more generally, we need 2Wq operations in q dimensions, where we consider that a multiplication is worth an addition.

To this cost, one must add (qW) times the cost of the evaluation of the separable synthesis function. When the latter is piecewise polynomial, on average we need W/4 tests to determine which of the polynomial pieces to use. Once a polynomial is selected, evaluation by Horner's scheme further

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FIGURE 15 Comparison of synthesis functions of same support W = 4.

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FIGURE 15 Comparison of synthesis functions of same support W = 4.

 Synthesis function e2 (dB)
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