連続ウェーブレット変換によるスペクトル解析

Continuous wavelet transform can localize time and frequency components of signal. The quantity of the wavelet transform corresponds to the amplitude of the component, but it is seldom used for the measurement of amplitude. In this paper, the calculation procedure of continuous wavelet transform of time series using fast Fourier transform algorithm is explained, and the scale parameter of wavelet transform is converted into period and frequency. The wavelet transforms of sinusoidal and chirp signals show that the resolution of wavelet transform decreases when the period or the frequency of signal increases, and the quantity of wavelet transforms of constant amplitude signals vary with period and frequency. Then, correction coefficient and logarithmic scaling of the scale parameter are introduced. Using these factors, the wavelet transform whose resolution and quantity are almost constant is obtained.