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The so-called tuned-correlated kernel (sometimes also called the first-orderstable spline kernel) is one of the most widely used kernels for theregularized impulse response estimation. This kernel can be derived by applyingan exponential decay function as a coordinate change to the first-order splinekernel. This paper focuses on this coordinate change and derives new kernels byinvestigating other coordinate changes induced by stable and strictly propertransfer functions. It is shown that the corresponding kernels inheritproperties from these coordinate changes and the first-order spline kernel. Inparticular, they have the maximum entropy property and moreover, the inverse oftheir Gram matrices has sparse structure. In addition, the spectral analysis ofsome special kernels are provided. Finally, a numerical example is given toshow the efficacy of the proposed kernel.

On the Coordinate Change to the First-Order Spline Kernel for Regularized Impulse Response Estimation