Discrete sampling formulas on spaces of \(p^{M}\)-periodic sequences for computational applications on edge detection. (English) Zbl 1077.94009
The authors introduce the notion of multiresolution analysis on the discrete sequence space. Based on it, sampling theorems are derived and truncation errors are estimated. These results can be compared with G. Walter’s theorem in functional spaces. In addition, one application for edge detection is given.
Reviewer: Youming Liu (Beijing)
MSC:
94A20 | Sampling theory in information and communication theory |
65T60 | Numerical methods for wavelets |
68T10 | Pattern recognition, speech recognition |
42C15 | General harmonic expansions, frames |
Keywords:
sampling formula; periodic sequences; multisolution analysis; discrete Fourier transform; edge detectionReferences:
[1] | Atreas N., J. Comp. Anal. Appl. 4 pp 89– (2000) |
[2] | Butzer P. L., Jber. d. Dt. Math.-Verein 90 pp 1– (1988) |
[3] | Briggs W. L., The DFT. An Owner’s Manual for the Discrete Fourier Transform (1995) · Zbl 0827.65147 · doi:10.1137/1.9781611971514 |
[4] | DOI: 10.1063/1.4823126 · doi:10.1063/1.4823126 |
[5] | DOI: 10.1007/978-3-642-59901-9 · doi:10.1007/978-3-642-59901-9 |
[6] | DOI: 10.1137/1.9781611970104 · Zbl 0776.42018 · doi:10.1137/1.9781611970104 |
[7] | Jerri A., Advanced Topics in Shannon Sampling and Interpolation Theory (1993) |
[8] | Higgins J. R., Sampling Theory in Fourier and Signal Analysis. Foundations (1996) · Zbl 0872.94010 |
[9] | Holschneider M., Wavelets an Analysis Tool (1995) · Zbl 0874.42020 |
[10] | Karanikas C., Proceedings of the Conference ”Applied Nonlinear Dynamics: from Semiconductors to Information Technologies” (Thessaloniki, 2001) 17 pp 195– (2003) |
[11] | DOI: 10.1007/BF02570568 · Zbl 0734.46019 · doi:10.1007/BF02570568 |
[12] | Papoulis A., Signal Analysis (1977) · Zbl 0422.94001 |
[13] | Young R. M., An Introduction to Non-Harmonic Fourier Series (1980) |
[14] | Walter G. G., Wavelets and Other Orthogonal Systems with Applications (1994) · Zbl 0866.42022 |
[15] | DOI: 10.1109/18.119745 · Zbl 0744.42018 · doi:10.1109/18.119745 |
[16] | Zayed A. I., Advances in Shannon’s Sampling Theory (1993) · Zbl 0868.94011 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.