Extension of the concept of multi-legged-type signals to the optimum multidimensional running approximation of multidimensional band-limited signals

Yuichi Kida; Takuro Kida

doi:10.1117/12.893822

8 September 2011 Extension of the concept of multi-legged-type signals to the optimum multidimensional running approximation of multidimensional band-limited signals

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 8136, Mathematics of Data/Image Pattern Coding, Compression, and Encryption with Applications XIII; 813607 (2011) https://doi.org/10.1117/12.893822
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

The minimization of approximation errors in a FIR multi-dimensional filter bank for band-limited signals is the important problem of multi-dimensional signal processing. In this paper, we consider the interpolation approximation that is modeled as a certain multi-dimensional FIR filter bank. Firstly, we introduce the known optimum approximation of multi-dimensional signals in FIR filter banks using a finite number of sample values. Secondly, we explain briefly a new concept of multi-legged-type signal that is a combined-signal of many one-dimensional band-limited signals. Backbone of this multi-legged-type signal is constituted with a set of small separable segments of the above one-dimensional signals that are determined by the proposed running approximation. Thirdly, we extend this concept to multi-dimensional hyper signal space. Based on this concept, we present an approximation method of the extended multi-dimensional multi-legged-type signals and we prove that this approximation in the hyper domain is the optimum. Finally, we define measures of error that become the proposed measures of error in the position of the backbone made by the corresponding multi-dimensional running approximation and become small about the other errors. Based on these measures of error, we prove that the presented multi-dimensional optimum approximation minimizes various continuous worst-case measures of the running approximation error at the same time.

Citation Download Citation

Yuichi Kida and Takuro Kida "Extension of the concept of multi-legged-type signals to the optimum multidimensional running approximation of multidimensional band-limited signals", Proc. SPIE 8136, Mathematics of Data/Image Pattern Coding, Compression, and Encryption with Applications XIII, 813607 (8 September 2011); https://doi.org/10.1117/12.893822

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
12 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Zinc

Multidimensional signal processing

Radon

Fourier transforms

Finite impulse response filters

Filtering (signal processing)

Signal processing

Show All Keywords

Keywords/Phrases

Search In:

Publication Years