Decomposition and Reconstruction of Signal in Real-Time Spectral Analysis

Abstract

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