Signal Interpolator Design Using Weighted-Least-Squares Method
Keywords:
Signal processing, signal reconstruction, sinc function, re-sampling, signal interpolation, interpolator design.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.
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