Signal reconstruction from the magnitude or phase of a generalised wavelet transform

This paper considers signal reconstruction from a class of linear Time Frequency Representations (TFRs) referred to as the Generalised Wavelet Transform (GWT). This generalisation incorporates a number of linear TFRs, including the Short-Time Fourier Transform (STFT) and Wavelet Transform (WT). The problem addressed is that of constructing a time series from partial information regarding a GWT. Following the methodology previously employed for the STFT, a Least Squares (LS) approach for signal reconstruction from the magnitude of the GWT is presented. Along with a signal reconstruction algorithm using only the phase of the GWT. Examples are given illustrating the validity of these two algorithms.