New construction of wavelets base on floor function |
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| Authors: | Zulkifly Abbas S Vahdati M Tavassoli Kajani KA Atan |
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| Institution: | aLaboratory of Computational Science and Informatics, Institute for Mathematical Research, University Putra Malaysia, Serdang 43400, Selangor, Malaysia;bDepartment of Mathematics, Islamic Azad University, P.O. Box 81595-158, Khorasgan, Isfahan, Iran;cLaboratory of Theoretical Studies, Institute for Mathematical Research, University Putra Malaysia, Serdang 43400, Selangor, Malaysia |
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| Abstract: | In this paper, the properties of the floor function has been used to find a function which is one on the interval 0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine–Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions. |
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| Keywords: | Floor function Stepwise function Haar wavelet Sine– Cosine wavelet Block-Pulse functions Hybrid Fourier Block-Pulse functions |
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