We propose to use the Generalized Morse Wavelets (GMWs) instead of commonly-used Morlet (or Gabor) wavelets in the Scattering Transform Network (STN), which we call the GMW-STN, for signal classification problems. The GMWs form a parameterized family of truly analytic wavelets while the Morlet wavelets are only approximately analytic. The analyticity of underlying wavelet filters in the STN is particularly important for nonstationary oscillatory signals such as music signals because it improves interpretability of the STN representations by providing multiscale amplitude and phase (and consequently frequency) information of input signals. We demonstrate the superiority of the GMW-STN over the conventional STN in music genre classification using the so-called GTZAN database. Moreover, we show the performance improvement of the GMW-STN by increasing its number of layers to three over the typical two-layer STN.}