Constant-Q signal analysis and synthesis

A generalization of the short-time Fourier transform is presented which performs constant-percentage bandwidth analysis of time-domain signals. The transform is shown to exhibit frequency-dependent time and frequency resolution. A synthesis transform is also developed which provides an analysis-synthesis system which is an identity in the absence of spectral modification (given a mild analysis window constraint). The effect of stationary multiplicative modifications is discussed. Finally, similarities between the constant-Q spectral domain and the human auditory system are explored, and some implications for acoustic signal processing mentioned.