In Real Time Spectral Analysis Method, Improvement of Frequency Resolution by Multistage Analysis

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 as the elastic function of the mother wavelet of wavelet transform, and the same effective analysis as wavelet transform is carried out. Since the processing of this analysis is independent almost completely, approximately complete parallel processing is possible. Analysis in real time is carried out by introducing parallel processing. In this analytical method, we use a sine wave and cosine wave of plural periods, and so we call these waves a cutting out wave and call the plural periods a number of periods. We use inner product of the cutting out wave and the signal. The number of periods determines the size of the width of time-window. If width of time-window is enlarged, frequency resolution will improve, but time resolution falls. It is impossible to improve the frequency resolution and the time resolution simultaneously. This is the uncertainty principle. In this analyzing method, it's analyzed by many signal detection unit. At first a signal is performed by all signal detection units, and I call this first stage analysis. Next we analyze the wave that appears in each signal detection unit in first stage by using the same signal detection unit again. This is second-stage analysis . This is repeated and plural stage analyses are conducted. This is multi-stage analysis. It is shown that the frequency resolution can be improved in spite of uncertainty principle by this multistage analysis.