“…Such Gabor functions have been previously used for analyzing auditory signals by several authors, including (Wolfe et al 2001, Kleinschmidt 2002, Kleinschmidt & Gelbart 2002, Lobo & Loizou 2003, Qiu et al 2003, van de Boogart & Lienhart 2006, Ezzat et al 2007, Domont et al 2008, He et al 2009, Heckmann et al 2011, Wu et al 2011, Schädler et al 2012, Sameh & Lachiri 2013. Our theory provides a new way of deriving this form of representation with special emphasis on the multi-scale nature of the Gaussian window functions and their resulting cascade properties between spectrograms at different temporal scales.…”