A new class of discrete orthogonal polynomials for blind fitting of finite data

被引：18

作者：

Morales-Mendoza, Luis J. ^{[1
]}

Gamboa-Rosales, Hamurabi ^{[2
]}

Shmaliy, Yuriy S. ^{[3
]}

机构：

[1] Univ Veracruzana, Dept Elect Engn, Poza Rica 93390, Mexico

[2] Univ Autonoma Zacatecas, Dept Elect Engn, Zacatecas 98000, Mexico

[3] Univ Guanajuato, Dept Elect Engn, Salamanca 36855, Gto, Mexico

来源：

SIGNAL PROCESSING | 2013年 / 93卷 / 07期

关键词：

Unbiased finite impulse response; Discrete orthogonal polynomials; Approximation; Analysis; IMAGE-ANALYSIS; FIR FILTER; MOMENTS; PREDICTORS; SPEECH; MODELS;

D O I：

10.1016/j.sigpro.2013.01.023

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We show that the polynomial unbiased finite impulse response (UFIR) functions derived by Shmaliy establish a new class of a one-parameter family of discrete orthogonal polynomials (DOP). The most noticeable distinction of these polynomials with respect to the classical Meixner, Charlier, Hahn, and Krawtchouk DOP is dependence on only one parameter the length of finite data. This makes them highly attractive for L-order blind fitting and analysis of informative processes. Properties of the UFIR polynomials are considered in detail along with the moments and recurrence relation. Examples of applications are given to blind approximation and phoneme pitch analysis. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：1785 / 1793

页数：9

共 50 条

[1] A New Class of Discrete Orthogonal Polynomials for Blind Fitting of Finite Data
Gamboa-Rosales, Hamurabi
Morales-Mendoza, Luis J.
Shmaliy, Yuriy S.
2013 10TH INTERNATIONAL CONFERENCE ON ELECTRICAL ENGINEERING, COMPUTING SCIENCE AND AUTOMATIC CONTROL (CCE), 2013, : 185 - 190
[2] DISCRETE SEMICLASSICAL ORTHOGONAL POLYNOMIALS OF CLASS ONE
Dominici, Diego
Marcellan, Francisco
PACIFIC JOURNAL OF MATHEMATICS, 2014, 268 (02) : 389 - 411
[3] A NEW CLASS OF ORTHOGONAL POLYNOMIALS
NEVAI, P
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 91 (03) : 409 - 415
[4] A NEW CLASS OF ORTHOGONAL POLYNOMIALS - THE BESSEL POLYNOMIALS
KRALL, HL
FRINK, O
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 65 (JAN) : 100 - 115
[5] A NEW CLASS OF ORTHOGONAL POLYNOMIALS - THE BESSEL POLYNOMIALS
KRALL, HL
FRINK, O
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1948, 54 (07) : 636 - 636
[6] UPDATING AND DOWNDATING OF ORTHOGONAL POLYNOMIALS WITH DATA FITTING APPLICATIONS
ELHAY, S
GOLUB, GH
KAUTSKY, J
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1991, 12 (02) : 327 - 353
[7] SWAC EXPERIMENTS ON THE USE OF ORTHOGONAL POLYNOMIALS FOR DATA FITTING
ASCHER, M
FORSYTHE, GE
JOURNAL OF THE ACM, 1958, 5 (01) : 9 - 21
[8] Two finite hypergeometric sequences of discrete orthogonal polynomials
Masjed-Jamei, Mohammad
Koepf, Wolfram
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (09) : 1429 - 1443
[9] Unbiased impulse responses - a class of discrete orthogonal polynomials
2005, ICIC Express Letters Office, Tokai University, Kumamoto Campus, 9-1-1, Toroku, Kumamoto, 862-8652, Japan (07):
[10] A basic class of symmetric orthogonal polynomials of a discrete variable
Masjed-Jamei, Mohammad
Area, Ivan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 399 (01) : 291 - 305

← 1 2 3 4 5 →