Determination of electrochemical impedance of lithium ion battery from time series data by wavelet transformation -Uncertainty of resolutions in time and frequency domains-

This paper presents theory and method of impedance determination by the wavelet transformation. The complex Morlet mother wavelet (CMMW), which is a product of sinusoidal wave and Gaussian time-window, was used to calculate the complex numbers of wavelet coefficient from the time domain data. An impedance spectrum was determined from wavelet coefficients transformed from current and voltage time series. The frequency resolution was defined by using the standard deviation, and could be controlled by the band parameter fb in CMMW. The large fb level means high frequency resolution and low time resolution. This fact means an uncertainty of resolutions in time and frequency domains. The proposed impedance determination from simple signals like a current step and the voltage response was applied to lithium ion battery (LIB). An impedance spectrum of LIB was determined form the time series data of discharge current and voltage response by the WT. And the amplitude of frequency resolution was indicated by error bar in the Bode diagram of impedance spectrum.