Interpolator using a plurality of polynomial equations and associated methods

摘要

An interpolator includes: a first quadratic coefficient generator for generating a first coefficient set fitting a first quadratic equation to input samples y.sub.0, y.sub.1 and y.sub.2 at x.sub. -1, x. sub.0, and x. sub.1, respectively; a second quadratic coefficient generator for generating a second coefficient set fitting a second quadratic equation to input samples y.sub.1, y.sub.2 and y.sub.3 at x. sub.0, x.sub.1 and x. sub.2, respectively; a bi-quadratic coefficient generator for generating a bi-quadratic coefficient set based upon the first and second coefficient sets; and an output circuit for generating an interpolated value for between x.sub.0 and x.sub.1 based upon the bi- quadratic coefficient set. The bi-quadratic generator preferably generates the bi- quadratic coefficient set based upon an average of the first and second coefficient sets. Accordingly, the bi-quadratic coefficient set of b.sub. 0, b.sub.1 and b.sub.2 is given by b.sub.0 =y. sub.1, b.sub.1 =(-y.sub.3 + 5y.sub.2 -3y.sub.1 -y.sub.0)/4, and b.sub.2 =(y.sub.3 -y.sub.2 -y.sub.1 + y.sub.0)/4. The interpolated value y(&Dgr; x) is equal to b.sub.0 +. DELTA.x(b.sub.1 +&Dgr;xb.sub.2). Polynomial coefficient generators may be used for polynomial equations of orders higher than two as in the quadratic equations. In addition, method aspects of the invention are also disclosed.