General-form 3-3-3 interpolation kernel and its simplified frequency-response derivation |
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Authors: | Tian-Bo Deng |
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Affiliation: | Department of Information Science, Faculty of Science, Toho University, Funabashi, Chiba, Japan |
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Abstract: | An interpolation kernel is required in a wide variety of signal processing applications such as image interpolation and timing adjustment in digital communications. This article presents a general-form interpolation kernel called 3-3-3 interpolation kernel and derives its frequency response in a closed-form by using a simple derivation method. This closed-form formula is preliminary to designing various 3-3-3 interpolation kernels subject to a set of design constraints. The 3-3-3 interpolation kernel is formed through utilising the third-degree piecewise polynomials, and it is an even-symmetric function. Thus, it will suffice to consider only its right-hand side when deriving its frequency response. Since the right-hand side of the interpolation kernel contains three piecewise polynomials of the third degree, i.e. the degrees of the three piecewise polynomials are (3,3,3), we call it the 3-3-3 interpolation kernel. Once the general-form frequency-response formula is derived, we can systematically formulate the design of various 3-3-3 interpolation kernels subject to a set of design constraints, which are targeted for different interpolation applications. Therefore, the closed-form frequency-response expression is preliminary to the optimal design of various 3-3-3 interpolation kernels. We will use an example to show the optimal design of a 3-3-3 interpolation kernel based on the closed-form frequency-response expression. |
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Keywords: | Interpolation general-form interpolation kernel 3-3-3 interpolation kernel frequency-response formula vector-form frequency-response expression |
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