A Framework for Invertible, Real-Time Constant-Q Transforms

Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency bands is preferable. This paper introduces a framework for efficient implementation of invertible signal transforms allowing for non-uniform frequency resolution. Non-uniformity in frequency is realized by applying nonstationary Gabor frames with adaptivity in the frequency domain. The realization of a perfectly invertible constant-Q transform is described in detail. To achieve real-time processing, independent of signal length, slice-wise processing of the full input signal is proposed and referred to as sliCQ transform. By applying frame theory and FFT-based processing, the presented approach overcomes computational inefficiency and lack of invertibility of classical constant-Q transform implementations. Numerical simulations evaluate the efficiency of the proposed algorithm and the method's applicability is illustrated by experiments on real-life audio signals.