In Real Time Spectral Analysis, Simultaneous Improvement of Both Time Resolution and Frequency Resolution by the Multi-stage Analysis, and Signal Reconstruction

Abstract

In recent years, analytical method in which the length of time-window for time-localization can be established optionally was shown by the authors. If you decide the time-window width which is in inverse proportion to the frequency, The function becomes the same function as the elastic function of the mother wavelet of wavelet transform, Effective analysis is carried out from low frequency to high frequency. In this analytical method, I use a signal detection unit to detect a signal. Frequency to detect a signal is set in the signal detection unit and I call it established frequency. In this analytical method, a lot of signal detection units which have different established frequency are used. First of all, all signal detection units analyze a signal as an analysis object. This is the analysis of the first stage. The wave which appears to each signal detection unit provided by the analysis of the first stage is analyzed by the signal detection unit. This is the second stage analysis. I repeat this, and multi-stage analysis is carried out. Until now, it was shown that the displacement in the time axes direction occurred at each signal detection unit in each stage analysis in the multi-stage analysis. In this paper, it is showed that new phase to produce at each signal detection unit in one analysis in the multi-stage analysis is the same as the displacement of time axes direction. Until now, there were amplitude characteristic and a phase characteristic as the condition to get a reconstruction wave. A phase characteristic disappears by revising the displacement at time axes direction and shows that it becomes only the amplitude characteristic. In addition, it shows that a reconstruction wave composes a signal waveform with high precision in a numerical analysis example using the Japanese vocal sound.