earticle

영어

This text starts with the short time Fourier transform and continuous wavelet transform to deduce the generalized S-transformation. From the point of generation views, we analyzed a relative relationship between generalized S-transformation and the short time Fourier transform, and the other relative relationship between generalized S transform and continuous wavelet transform. The article gives the definition of “the gene mutation of formula” and “the genetic restructuring of formula”, and introduces the deriving process of the two core concept. Theoretical analyses show that generalized S-transformation inherited the desirable characteristics in short time Fourier transform which use the window function to select suitable signal. Through genome sequencing of specific parameters, generalized S-transformation has a stronger adaptation that the time-frequency window could make real-time adjusting of frequency. Moreover, generalized S-transformation breaks out limitation that the wavelet function has to content the admissible conditions. From the point of gene mutation, we give the definition of “the gene mutation of formula”. Based on the structure form of wavelet functions, we define the generalized S-transformation with a wider domain of definition. Generalized S-transformation inherited the desirable characteristics of the short time Fourier transform and continuous wavelet transform. It has great utility and flexibility in analyzing non-stationary signals.