The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 52-462
Full Name: Jalal Karam
Position: Associate Professor
Age: ON
Sex: Male
Address: Alfaisal University, Riyadh.
Country: SAUDI ARABIA
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E-mail address: jkaram@alfaisal.edu
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Title of the Paper: Locating zeros of polynomials associated with Daubechies orthogonal wavelets
Authors as they appear in the Paper: Jalal Karam
Email addresses of all the authors: jkaram@alfaisal.edu
Number of paper pages: 10
Abstract: In the last decade, Daubechies orthogonal wavelets have been successfully used and proved their practicality in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, the low pass and high pass filters that generate a Daubechies mother wavelet are considered. From these filters, a new set of high pass and low pass filters are derived by using the "Alternating Flip" techniques. The new set of filters maintain perfect reconstruction status of an input signal, thus allowing the construction of a new mother wavelet and a new scaling function that are reflective to those of the originals. Illustration are given and new reflective wavelets are derived. Also, a subclass of polynomials is derived from this construction process!
by considering the ratios of consecutive binomial polynomials' coefficients. A mathematical proof of the residency of the roots of this class of polynomials inside the unit circle is presented along with an illustration for $db6$, a member of the Daubechies orthogonal wavelets family. The kakeya-Enestrom theorem is discussed along with some of its generalizations. Finally, a $\lambda$-dependent difference among the coefficients of the new set of polynomials is examined and optimized locations of the roots are derived.
Keywords: Zeros, Polynomials, Daubechies Orthogonal Wavelets, Reflective Wavelets, Kakeya-Enestrom Theorem.
EXTENSION of the file: .pdf
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How Did you learn about congress: Applied Mathematics, Wavelets Construction, Location of Zeros of Polynomials
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