Wavelet transform for time-frequency representation and filtration of discrete signals

A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where ${\displaystyle N=2^p}$, p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet spectrum and the classical discrete Fourier transform between the time and the frequency domains.