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

TL;DR

This paper presents a novel, efficient, invertible constant-Q transform framework for real-time audio processing that allows non-linear frequency resolution using nonstationary Gabor frames and slice-wise processing.

Contribution

It introduces a new invertible, non-uniform constant-Q transform framework with real-time, slice-wise implementation based on nonstationary Gabor frames and FFT processing.

Findings

Achieves perfect invertibility of constant-Q transform.

Enables real-time processing independent of signal length.

Demonstrates effectiveness on real-life audio signals.

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.