Sliding with a Constant Q

The linear frequency (constant-bandwidth) scale of the FFT has long been recognised as a disadvantage for audio processing. Long analysis windows are required for adequate low-frequency resolution, while small windows offer lower latency, better handling of transients, and reduced computation cost. A constant-Q form of analysis offers the possibility of increased low-frequency resolution for a given window size, this resolution being essential for many fundamental processing tasks such as pitch shifting. We consider the application of the Sliding Discrete Fourier Transform to a Constant-Q analysis. The increased flexibility of sliding allows for a variety of data alignments, and we produce the mathematical formulation of these. Windowing in the frequency domain introduces further complications. Finally we consider the implementation of the analysis on both serial and parallel computers.