Musical applications using perfect-translation-invariant variable-density complex discrete wavelet transform

In this paper, firstly, we introduce our proposed complex discrete wavelet transform achieving variable wavelet density in the frequency and time domains with perfect translation invariance. Next, using it, we introduce three musical applications “High-precision frequency detection”, “Time stretch” and “Pitch shift”. The time stretch is the process of changing the speed of an audio signal without affecting its pitch, and the pitch shift is the process of changing the pitch without affecting the speed.