Gamma splines and wavelets

Hannu Olkkonen, Juuso T. Olkkonen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.
Original languageEnglish
Article number625364
Number of pages8
JournalJournal of Engineering
Volume2013
DOIs
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed

Fingerprint

Splines
Multiresolution analysis
Signal analysis
Impulse response
Electrocardiography
Convolution
Wavelet transforms
Interpolation
Signal processing
Decomposition

Cite this

Olkkonen, H., & Olkkonen, J. T. (2013). Gamma splines and wavelets. Journal of Engineering, 2013, [625364]. https://doi.org/10.1155/2013/625364
Olkkonen, Hannu ; Olkkonen, Juuso T. / Gamma splines and wavelets. In: Journal of Engineering. 2013 ; Vol. 2013.
@article{6491a289eaa340ce82184051cd2e377b,
title = "Gamma splines and wavelets",
abstract = "In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.",
author = "Hannu Olkkonen and Olkkonen, {Juuso T.}",
year = "2013",
doi = "10.1155/2013/625364",
language = "English",
volume = "2013",
journal = "Journal of Engineering",
issn = "2314-4904",
publisher = "Hindawi Limited",

}

Olkkonen, H & Olkkonen, JT 2013, 'Gamma splines and wavelets', Journal of Engineering, vol. 2013, 625364. https://doi.org/10.1155/2013/625364

Gamma splines and wavelets. / Olkkonen, Hannu; Olkkonen, Juuso T.

In: Journal of Engineering, Vol. 2013, 625364, 2013.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Gamma splines and wavelets

AU - Olkkonen, Hannu

AU - Olkkonen, Juuso T.

PY - 2013

Y1 - 2013

N2 - In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.

AB - In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.

U2 - 10.1155/2013/625364

DO - 10.1155/2013/625364

M3 - Article

VL - 2013

JO - Journal of Engineering

JF - Journal of Engineering

SN - 2314-4904

M1 - 625364

ER -