Abstract
Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools. An approach for designing a sort of orthogonal super-wavelet wraps in three-dimensional space is presented and their orthogonality traits are characterized by virtue of iteration method and time-frequency representation method. The orthogonality formulas concerning these super-wavelet wraps are established. Moreover, it is shown how to draw new Riesz bases of space L 2(R 3) from these wavelet wraps. The trivariate dual frames is also discussed.
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References
Telesca, L., et al.: Multiresolution wavelet analysis of earthquakes. Chaos, Solitons & Fractals 22, 741–748 (2004)
Iovane, G., Giordano, P.: Wavelet and multiresolution analysis:Nature of ε ∞ Cantorian space-time. Chaos, Solitons & Fractals 32(4), 896–910 (2007)
Zhang, N., Wu, X.: Lossless Compression of Color Mosaic Images. IEEE Trans. Image Processing 15(16), 1379–1388 (2006)
Chen, Q., et al.: A study on compactly supported orthogo-nal vector-valued wavelets and wavelet packets. Chaos, Solitons & Fractals 31(4), 1024–1034 (2007)
Shen, Z.: Nontensor product wavelet packets in L 2(R s). SIAM Math. Anal. 26(4), 1061–1074 (1995)
Chen, Q., Huo, A.: The research of a class of biorthogonal compactly supported vector-valued wavelets. Chaos, Solitons & Fractals 41(2), 951–961 (2009)
Li, S., et al.: A Theory of Geeneralized Multiresolution Structure and Pseudoframes of Translates. J. Fourier Anal. Appl. 6(1), 23–40 (2001)
Chen, Q., Shi, Z.: Construction and properties of orthogonal matrix-valued wavelets and wavelet packets. Chaos, Solitons & Fractals 37(1), 75–86 (2008)
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© 2013 Springer-Verlag Berlin Heidelberg
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Gao, H., Lu, J. (2013). The Characterization of the Trivariate Super-Wavelet Wraps and Applications in Electronic Engineering. In: Jin, D., Lin, S. (eds) Advances in Mechanical and Electronic Engineering. Lecture Notes in Electrical Engineering, vol 178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31528-2_32
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DOI: https://doi.org/10.1007/978-3-642-31528-2_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31527-5
Online ISBN: 978-3-642-31528-2
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