The unified mathematical model of transforms in signal processing

At present, there exist many transformation methods in signal analysis and there is an increasing number of methods being developed. It is of great importance to study how to grasp transformation methods of signal analysis and how to implement them by using software on a computer. In this paper an attempt is made to build a unified mathematical model for signal transformations. Concepts such as domain variable, domain variable function, transform kernel function etc. are given and the unified mathematical model of the Fourier transform, the short time Fourier transform and the wavelet transform are studied and established. Furthermore, the flowchart of the model is given and the physical meaning of the model is described. Finally the values of the parameters and parameter functions of Fourier transform, short time Fourier transform and wavelet transform in the model are given in this paper.