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A Foundational Inspection of Wavelet Analysis

Yoshiyuki HOSOKAI, Hiroshi SAKAMOTO, Tatsuo NAGASAKA, Isao YANAGAWA,
Masatoshi SASAKI, Mikio OISHI*, Haruo OBARA*, Choichiro SUNOUCHI**
and Masayuki ZUGUCHI*

Department of Radiology, Tohoku University Hospital
*Department of Radiological Technology, College of Medical Sciences, Tohoku University
**General Education, College of Medical Sciences, Tohoku University


Key words : Wavlet, Multi-Resolution Analysys, Discrete Wavlet Transform,
Center Frequency, Frequency Response Characteristic


      Recently, much attention has been paid to Wavelet analysis as a way of processing signal data. Wavelet analysis, which makes good use of Fourier analysis in that signal data are described in frequency domains, allows temporal frequency analysis by capturing temporal or spatial transition in frequency domains. This means that the positional information on a certain frequency domain, that is, the information as to where a certain frequency appears in signal data can be obtained, and this kind of information cannot be obtained in Fourier analysis.
      However, the theoretical aspects of Wavelet analysis are very difficult to understand, and it is a long way to its application. Then, in this article, we will explain about the minimum aspects essential to the application of Wavelet analysis in order to make the analysis as a whole easy to understand. In addition, we will examine the frequency characteristics of Mother Wavelet and Scaling functions so that we can specify a Mother Wavelet which is most appropriate for the data to be analyzed.