A framework for invertible, real-time constant-Q transforms

Online resources accompanying the research paper:

N. Holighaus, M. Dörfler, G. A. Velasco, and T. Grill, “A framework for invertible, real-time constant-Q transforms," IEEE Transactions on Audio, Speech and Language Processing, 21(4):775-785, 2013.

Abstract. 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 and in particular non-linear 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.

Online resources:

Sliced constant-Q experiments
Comparison of STFT and CQ-NSGT
Component transposition
Example filters