Current Search: Signal processing--Mathematical models (x)
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Title
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Discrete signal representation using triangular basis functions.
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Creator
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Nallur, Padmanabha., Florida Atlantic University, Hartt, William H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
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Abstract/Description
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This thesis deals with the representation of discrete signals using triangular basis functions. Signals are usually represented by Fourier series expansions where the basis functions are cosine and sine functions which are all mutually orthogonal. The triangular basis functions used here are called TRIC (triangular cosine) and TRIS (triangular sine) functions. The TRIC and TRIS functions are like their cosine and sine function counterparts except that they are linear. The TRIC and TRIS...
Show moreThis thesis deals with the representation of discrete signals using triangular basis functions. Signals are usually represented by Fourier series expansions where the basis functions are cosine and sine functions which are all mutually orthogonal. The triangular basis functions used here are called TRIC (triangular cosine) and TRIS (triangular sine) functions. The TRIC and TRIS functions are like their cosine and sine function counterparts except that they are linear. The TRIC and TRIS functions are not all mutually orthogonal, though most of them are. A matrix method of representing discrete signals using TRIC and TRIS functions is presented. A discrete triangular transform matrix is developed and a method of deriving this matrix is presented. A Fortran program is written to derive the discrete triangular transform matrix and to prove the reconstruction of several basic functions like impulse, step, pulse and sinusoidal waveforms.
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Date Issued
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1988
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PURL
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http://purl.flvc.org/fcla/dt/14451
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Subject Headings
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Signal processing--Mathematical models
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Format
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Document (PDF)
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Title
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Non-separable two dimensional wavelets and their filter banks in polar coordinates.
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Creator
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Andric, Oleg., Florida Atlantic University, Erdol, Nurgun
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Abstract/Description
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The problems encountered in development and implementation of orthonormal two dimensional wavelet bases and their filter banks in polar coordinates are addressed. These wavelets and filter banks have possible applications in processing signals that are collected by sensors working in the polar coordinate system, such as biomedical and radar generated signals. The relationship between the space of measurable, square-integrable functions on the punctured polar coordinate system L^2(P) and space...
Show moreThe problems encountered in development and implementation of orthonormal two dimensional wavelet bases and their filter banks in polar coordinates are addressed. These wavelets and filter banks have possible applications in processing signals that are collected by sensors working in the polar coordinate system, such as biomedical and radar generated signals. The relationship between the space of measurable, square-integrable functions on the punctured polar coordinate system L^2(P) and space of measurable, square-integrable functions on the rectangular plane L^2(R^2) is developed. This allows us to develop complete wavelet bases in a more convenient and familiar surrounding of L^2(R^2) and to transport this theory to L^2(P). Corresponding filter banks are also developed. The implementation of wavelet analysis of punctured polar plane is discussed. An example of wavelet bases, filter banks, and implementation is provided.
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Date Issued
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1995
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PURL
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http://purl.flvc.org/fcla/dt/15190
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Subject Headings
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Wavelets (Mathematics), Coordinates, Polar, Signal processing--Mathematical models
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Format
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Document (PDF)
