Signal reconstruction from a generalised wavelet transform

This paper presents a generalisation of the traditional wavelet transform (WT) called the Generalised Wavelet Transform (GWT). This generalisation incorporates a number of linear Time-Frequency Representations (TFRs), including the Short-Time Fourier Transform (ST-FT) and WT. This paper addresses the problem of signal reconstruction from an arbitrary GWT. In order to be robust to modifications of the TFR, a Minimum Least Squares (MLS) approach to signal reconstruction is presented. This results in a method for reconstructing a MLS signal from a modified or altered GWT.