Interpolator and designing method thereof

An interpolation device which calculates a pixel value f(x) of a new pixel Q defined at an arbitrary position in an interpolation interval both ends of which are at two adjacent pixels by performing interpolation using a cubic polynomial “f(x)=Ax3+Bx2+Cx+D” concerning a position x based on a one-dimensional pixel array obtained by arranging a plurality of pixels having predetermined pixel values at predetermined pitches, comprising:

• a data input unit which inputs pixel values of sample pixels and the position x of the new pixel Q when the two adjacent pixels are defined as interval terminal pixels, “a predetermined number of pixels to be used for interpolation” continuously arranged adjacent to each other on the left of the interpolation interval are defined as left side interpolation pixels, “a predetermined number of pixels to be used for interpolation” continuously arranged adjacent to each other on the right of the interpolation interval are defined as right side interpolation pixels, and S (S>4) in total of pixels consisting of the interval terminal pixels, the left side interpolation pixels, and the right side interpolation pixels are defined as sample pixels;
• a weighting coefficient storage unit which stores weighting factors for the sample pixels, indicating weighting according to the distances from the interpolation interval;
• a left side influence factor arithmetic unit which calculates left side influence factors indicating influences of pixel values of the left side interpolation pixels on coefficients of the cubic polynomial based on the pixel values of the left side interpolation pixels and the weighting factors;
• a right side influence factor arithmetic unit which calculates right side influence factors indicating influences of pixel values of the right side interpolation pixels on coefficients of the cubic polynomial based on the pixel values of the right side interpolation pixels and the weighting factors;
• and
• an interpolated value arithmetic unit which determines auxiliary coefficients a, b, c, and d defined so as to satisfy A=(a−b), B=(b−c), C=(c−d), and D=d instead of the coefficients A, B, C, and D by using the pixel values of the interval terminal pixels, the left side influence factors, the right side influence factors, and the weighting factors, and calculates the pixel value f(x) by an arithmetic operation by a cubic polynomial of “f(x)=[{ax+b(1−x)}x+c(1−x)]x+d(1−x)” for which the position x is substituted instead of the cubic polynomial “f(x)=Ax3+Bx2+Cx+D.”