Spectral characteristics of two parameter fifth degree polynomial convolution kernel

Milivojević, Zoran N.; Savić, Nataša; Prlinčević, Bojan

doi:10.5937/bnsr12-38771

Cited by 1 publication

(6 citation statements)

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“…where α and β are kernel parameters. The 2P kernel can be presented in the form (Milivojević et al, 2022):…”

Section: Two Parameter Fifth-order Kernelmentioning

confidence: 99%

“…Current solutions, which are proposed for use in DSP, are interpolation kernels of small lengths, which are defined on the segment [-L, L], where L ≤ 8. In addition, in order to increase the speed of interpolation, it is desirable that the kernel is presented as a mathematical function of low complexity (Milivojević et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

“…Interpolation polynomial kernels are extremely relevant. The chronology of the development of the polynomial kernels is detailed in (Milivojević et al, 2022). Numerically, the least complex is the nearest-neighbor, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In the paper (Milivojević et al, 2022), the spectral characteristic of the 2P fifth order kernel was determined. The spectral characteristic of the 2P kernel is done as follows.…”

Section: Introductionmentioning

confidence: 99%

“…In the first part of the paper, the analytical form of the fifth order 2P interpolation kernel is described and the components of the kernel are shown. After that, the spectral components, which are determined by applying the Fourier transformation over the kernel components, are shown (Milivojević et al, 2022). The spectral characteristic of the 2P kernel is formed by spectral components.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of the 2P fifth degree convolution kernel in the spectral domain

Savić,

Milivojević,

Prlinčević

2023

Bull Nat Sci Research

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The first part of the paper describes a two-parameter (2P) fifth-order interpolation kernel, r. After that, from the 2P kernel, the kernel components were created. By applying the Fourier transformation to each kernel component, the spectral components of the 2P kernel were obtained. The spectral characteristic of the 2P kernel, H, was created from the spectral components. After that, the algorithm, that optimizes the parameters of the 2P kernel so as to eliminate the ripple of the spectral characteristics, is described. The optimization was performed in such a way that the spectral characteristic developed in the Taylor series, H T. With the condition for the elimination of the members of the Tylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (a opt , b opt) were determined. The second part of the paper describes an Experiment, in which the interpolation accuracy of the 2P kernel was tested. Convolution interpolation, with the 2P kernel, was performed over the signals from the Test base. The Test base is created with musical signals. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the precision of the interpolation was determined. The results (a opt , b opt , MSE min) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation precision with the proposed 2P interpolation kernel, compared to the interpolation precision with, 1P interpolation kernel. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

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“…where α and β are kernel parameters. The 2P kernel can be presented in the form (Milivojević et al, 2022):…”

Section: Two Parameter Fifth-order Kernelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the paper (Milivojević et al, 2022), the spectral characteristic of the 2P fifth order kernel was determined. The spectral characteristic of the 2P kernel is done as follows.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations