Decomposition and reconstruction of signal in high‐speed processing method of real‐time spectral analysis
Hideto Nakatsuji, S. Ōmatu · Electronics and Communications in Japan · 2011
Abstract In recent years, wavelet transforms based on multiresolution analysis have been considered as a concrete algorithm for an integral wavelet transform that performs spectral analysis in the time–frequency domain. On the other hand, we have proposed a new method of analysis that updates the spectrum using input data only. The new method consists of analysis approach 1, which is a fundamental analysis method, and analysis approach 2, which is an analysis method that achieves high‐speed processing. Decomposition and reconstruction of the signal based on analysis approach 1 has already been proposed by us. This paper describes the decomposition and reconstruction of a signal based on analysis approach 2. The decomposition wave in analysis approach 2 cannot be obtained by the same method as in the case of analysis approach 1, but requires mathematical processing. In the processing, the decomposition wave in analysis approach 2 is identical to the decomposition wave in analysis approach 1. Therefore, the decomposition and reconstruction of the signal in analysis approach 2 results in the decomposition and reconstruction of the signal in analysis approach 1. As an example of numerical analysis, we illustrate the decomposition and reconstruction of the Japanese vocal sound /i/. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(8): 47–56, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/ecj.10250