Robust and optimal control
Fractional Splines and Wavelets
SIAM Review
Optimal Sampled-Data Control Systems
Optimal Sampled-Data Control Systems
Image compression by linear splines over adaptive triangulations
Signal Processing
IEEE Transactions on Image Processing
Design of multirate filter banks by ℋ∞optimization
IEEE Transactions on Signal Processing
B-spline signal processing. I. Theory
IEEE Transactions on Signal Processing
B-spline signal processing. II. Efficiency design and applications
IEEE Transactions on Signal Processing
MIMO linear equalization with an H∞ criterion
IEEE Transactions on Signal Processing
Efficient implementation of all-digital interpolation
IEEE Transactions on Image Processing
Convolution-based interpolation for fast, high-quality rotation of images
IEEE Transactions on Image Processing
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In this paper, we give a causal solution to the problem of spline interpolation using H^~ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time applications. Our objective here is to derive a causal system which approximates spline interpolation by H^~ optimization for the filter. The advantage of H^~ optimization is that it can address uncertainty in the input signals to be interpolated in design, and hence the optimized system has robustness property against signal uncertainty. We give a closed-form solution to the H^~ optimization in the case of the cubic splines. For higher-order splines, the optimal filter can be effectively solved by a numerical computation. We also show that the optimal FIR (finite impulse response) filter can be designed by an LMI (linear matrix inequality), which can also be effectively solved numerically. A design example is presented to illustrate the result.