DocumentCode :
1093996
Title :
Evaluation of quantization error in two-dimensional digital filters
Author :
Agathoklis, P. ; Jury, E.I. ; Mansour, M.
Author_Institution :
Swiss Federal Institute of Techonolgy, Zurich, Switzerland
Volume :
28
Issue :
3
fYear :
1980
fDate :
6/1/1980 12:00:00 AM
Firstpage :
273
Lastpage :
279
Abstract :
In the evaluation of the quantization error in two-dimensional (2-D) digital filters, a procedure for computing {\\infty \\atop {\\sum \\atop m=0}} {\\infty \\atop {\\sum \\atop n=0}} y^{2}(m,n) = {1 \\over (2{\\pi}j)^{2}} \\oint \\oint Y(z_{1},z_{2}) Y(z_{1}^{-1},z_{2}^{-1}) {dz_{1}dz_{2} \\over z_{1}z_{2}} T^{2} = {(z_{1},z_{2}): |z_{1}|=1, |z_{2}|=1} is required. In this paper a condition for a finite quantization error is given and a discussion on the evaluation of the integral based on the residue method is presented. Examples for such an evaluation are given. Furthermore, the salient differences between the one-dimensional (1-D) complex integral evaluation and the two-dimensional one are discussed. Notation: We note with \\bar{U}^{2} = \\{(z_{1}, z_{2}): \\mid z_{1} \\mid \\leq 1, \\mid z_{2} \\mid \\leq 1 \\} } the closed unit bidisk, with u^{2} = {(z_{1}, z_{2}): |z_{1}| < 1, |z_{2}| \\leq 1} the open unit bidisk, and with T_{2} = {(z_{1}, z_{2}): |z_{1}| = 1, |z_{2}| = 1} the distinguished boundary of the unit bidisk. The 2-D z -transform is defined as Y(z_{1}, z_{2}) = \\sum_{m=0}^{\\infty} \\sum_{n=0}^{\\infty} y (m,n)z_{1}^{m}z_{2}^{n} .
Keywords :
Acoustics; Automatic control; Digital filters; Industrial electronics; Integral equations; Polynomials; Quantization; Sufficient conditions; Transfer functions; Two dimensional displays;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1980.1163403
Filename :
1163403
Link To Document :
https://search.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=1093996
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