Constant-Q transform

In mathematics and signal processing, the constant-Q transform and variable-Q transform, simply known as CQT and VQT, transforms a data series to the frequency domain. It is related to the Fourier transform and very closely related to the complex Morlet wavelet transform. Its design is suited for musical representation.

The transform can be thought of as a series of filters f_k, logarithmically spaced in frequency, with the k-th filter having a spectral width δf_k equal to a multiple of the previous filter's width:

${\displaystyle \delta f_{k}=2^{1/n}\cdot \delta f_{k-1}=\left(2^{1/n}\right)^{k}\cdot \delta f_{\text{min}},}$

where δf_k is the bandwidth of the k-th filter, f_min is the central frequency of the lowest filter, and n is the number of filters per octave.