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The Discrete Linear Chirp Transform and its Applications

Alkishriwo, Osama (2013) The Discrete Linear Chirp Transform and its Applications. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In many applications in signal processing, the discrete Fourier transform (DFT) plays a significant role in analyzing characteristics of stationary signals in the frequency domain. The DFT can be implemented in a very efficient way using the fast Fourier transform (FFT) algorithm. However, many actual signals by their nature are non--stationary signals which make the choice of the DFT to deal with such signals not appropriate. Alternative tools for analyzing non--stationary signals come with the development of time--frequency distributions (TFD). The Wigner--Ville distribution is a time--frequency distribution that represents linear chirps in an ideal way, but it has the problem of cross--terms which makes the analysis of
such tools unacceptable for multi--component signals. In this dissertation, we develop three definitions of linear chirp transforms which are: the continuous linear chirp transform (CLCT), the discrete linear chirp transform (DLCT), and the discrete cosine chirp transform (DCCT). Most of this work focuses on the discrete linear chirp transform (DLCT) which can be considered a generalization of the DFT to analyze non--stationary signals. The DLCT is a joint frequency chirp--rate transformation, capable of locally representing signals in terms of linear chirps. Important properties of this transform are discussed and explored. The efficient implementation of the DLCT is given by taking advantage of the FFT algorithm. Since this novel transform can be implemented in a fast and efficient way, this would make the proposed transform a candidate to be used for many applications, including chirp rate estimation, signal compression, filtering, signal separation, elimination of the cross--terms in the Wigner--Ville distribution, and in communication systems. In this dissertation, we will explore some of these applications.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChaparro, Luislfch@pitt.eduLFCH
Committee MemberMao, Zhi-Hongzhm4@pitt.eduZHM4
Committee MemberEl-Jaroudi, Amroamro@pitt.eduAMRO
Committee MemberSejdic, Ervinesejdic@pitt.eduESEJDIC
Committee MemberSun, Minguidrsun@pitt.eduDRSUN
Committee MemberManfredi, Juanmanfredi@pitt.eduMANFREDI
Date: 28 June 2013
Date Type: Publication
Defense Date: 7 March 2013
Approval Date: 28 June 2013
Submission Date: 13 March 2013
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 109
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Electrical Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Continuous linear chirp transform,Discrete cosine chirp transform, Discrete linear chirp transform, Signal compression, Compressive sensing, Time-frequency analysis, Empirical mode decomposition, Wigner-Ville distribution, Fractional Fourier transform, OFDM, Coupled OFDM, Capacity, Digital modulation, Sparsity.
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Date Deposited: 28 Jun 2013 19:39
Last Modified: 15 Nov 2016 14:10


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