Abstract—This paper shows that the bandwidth of a cubic interpolator can be designed by using a weighted least-squares (WLS) method in the frequency-domain. We first show how to construct a length-6 cubic whose support is 6 by connecting three piecewise polynomials of the third degree, and then explain how to find its optimal coefficients through minimizing the weighted squared error between the ideal and actual frequency responses of the length-6 cubic. By adjusting the weighting functions on different frequency bands, we can easily control the bandwidth of interest. In practical applications, according to the distribution of the signal to be interpolated, we can adjust the weighting function in the interpolator design and thus obtain very accurate frequency bands. As a consequence, the original band-limited analog signal can be accurately reconstructed, which also leads to high-accuracy signal interpolation. A narrow-band design example is given to illustrate that the length-6 cubic can achieve much higher accuracy frequency response than other existing interpolators. Moreover, we also detail how to choose the weighting function including ``don't care'' frequency bands.
Index Terms—Signal processing, signal reconstruction, sinc function, re-sampling, signal interpolation, interpolator design.
N. Ito is with the Department of Information Science, Faculty of Science, Toho University, Miyama 2-2-1, Funabashi, Chiba 274-8510, Japan (e-mail:firstname.lastname@example.org).
W. Qin is with Dalian Polytechnic University, China.
Cite: Noboru Ito and Wei Qin, "Signal Interpolator Design Using Weighted-Least-Squares Method," International Journal of Information and Electronics Engineering vol. 3, no. 3, pp. 299-303，2013.