Sinusoidal+Residual analysis/synthesis models have been developed for music
applications. They have been very successful and are already found in commercial and experimental tools
used by musicians as well as researchers. In this paper, we present the principles of this now
classical model. However, the standard version of the model suffers from limitations in various cases. We
discuss some improvements of the standard method designed in order to overcome these difficulties. We then
present and compare other analysis techniques which use Elementary Waveforms, i.e. waveforms localised
both on the frequency and the time axis. In particular, the High Resolution Matching Pursuit algorithm is
proposed as a potentially successful new direction of research.