Time-frequency digital filtering based on an invertible wavelet transform: an application to evoked potentials

This paper presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, we have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities.