Display Settings:

Format

Send to:

Choose Destination
See comment in PubMed Commons below
Digit Signal Process. 2010 Sep 1;20(5):1330-1340.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

Author information

  • 1Dept. of Electrical and Computer Engineering Technology, Western Carolina University, Cullowhee, NC 28723 USA ( ptay@email.wcu.edu ).

Abstract

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

PMID:
20694170
[PubMed]
PMCID:
PMC2914340
Free PMC Article
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for PubMed Central
    Loading ...
    Write to the Help Desk