Multiscale inverse filtering

The advantages of a time-scale analysis for the detection of transient signals are demonstrated. The transients discussed have a shape known to within a scale factor and may be partially overlapping. Only cases of high SNR (signal-to-noise ratio) are considered. After a short introduction to the wavelet transform, the links between detection and time-scale analysis are given. They are illustrated by a simulation example. A method, multiscale inverse filtering, that obtains a better separation of overlapping transients is then proposed. This technique is examined and criticized from a deconvolution point of view