Decomposition and Reconstruction of Signal in Real-Time Spectral Analysis

摘要

In recent years, wavelet transform which gives expression in the time-frequency domain has been adopted for a nonstationary process. The authors have proposed a new spectral analytical method in the time-frequency domain. In the conventional spectral analytical methods, the decomposition and the reconstruction of signals have been obtained analytically. The proposed method consists of two approaches. We call these approaches Approach 1 and Approach 2. In this paper, we show the decomposition and reconstruction of signals based on Approach 1. First, we show that the signal is decomposed to the signal elements. They are called the decomposition waves, and all of these decomposed waves are added to obtain the reconstructed wave. Next, we show the magnitude characteristic and the phase characteristic between the original signal and the reconstructed wave. Then the conditions between the signal and the reconstructed wave are derived to realize a sufficiently approximated wave. By a numeric calculation example, we show the approximation ability by the proposed method.