TY - JOUR
T1 - Algebraic signal processing theory
T2 - 1-D nearest neighbor models
AU - Sandryhaila, Aliaksei
AU - Kovačević, Jelena
AU - Püschel, Markus
N1 - Funding Information:
Manuscript received July 19, 2011; revised November 21, 2011 and January 16, 2012; accepted January 16, 2012. Date of publication January 26, 2012; date of current version April 13, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Antonio Napoli-tano. This work was supported in part by the NSF by Grant CCF-0634967.
PY - 2012/5
Y1 - 2012/5
N2 - We present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials. We demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest neighbor shift introduced in this paper. Using the algebraic signal processing theory, we construct signal models based on this shift and derive their corresponding signal processing concepts, including the proper notions of signal and filter spaces, z-transform, convolution, spectrum, and Fourier transform. The presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials.
AB - We present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials. We demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest neighbor shift introduced in this paper. Using the algebraic signal processing theory, we construct signal models based on this shift and derive their corresponding signal processing concepts, including the proper notions of signal and filter spaces, z-transform, convolution, spectrum, and Fourier transform. The presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials.
KW - Algebra
KW - Fourier transform
KW - Hermite polynomials
KW - Laguerre polynomials
KW - Legendre polynomials
KW - convolution
KW - filter
KW - module
KW - orthogonal polynomials
KW - shift
KW - signal model
KW - signal representation
UR - http://www.scopus.com/inward/record.url?scp=84860007987&partnerID=8YFLogxK
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U2 - 10.1109/TSP.2012.2186133
DO - 10.1109/TSP.2012.2186133
M3 - Article
AN - SCOPUS:84860007987
SN - 1053-587X
VL - 60
SP - 2247
EP - 2259
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 5
M1 - 6140984
ER -