Constant-q Transform Toolbox for Music Processing

This paper proposes a computationally efficient method for computing the constant-Q transform (CQT) of a timedomain signal. CQT refers to a time-frequency representation where the frequency bins are geometrically spaced and the Q-factors (ratios of the center frequencies to bandwidths) of all bins are equal. An inverse transform is proposed which enables a reasonable-quality (around 55dB signal-to-noise ratio) reconstruction of the original signal from its CQT coefficients. Here CQTs with high Q-factors, equivalent to 12–96 bins per octave, are of particular interest. The proposed method is flexible with regard to the number of bins per octave, the applied window function, and the Q-factor, and is particularly suitable for the analysis of music signals. A reference implementation of the proposed methods is published as a Matlab toolbox. The toolbox includes user-interface tools that facilitate spectral data visualization and the indexing and working with the data structure produced by the CQT.