In mathematics and signal processing, the constant-Q transform, simply known as CQT 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.
The transform can be thought of as a series of filters fk, logarithmically spaced in frequency, with the k-th filter having a spectral width δfk equal to a multiple of the previous filter's width:
δ f k = 2 1 / n ⋅ δ f k − 1 = ( 2 1 / n ) k ⋅ δ f min , {\displaystyle \delta f_{k}=2^{1/n}\cdot \delta f_{k-1}=\left(2^{1/n}\right)^{k}\cdot \delta f_{\text{min}},}where δfk is the bandwidth of the k-th filter, fmin is the central frequency of the lowest filter, and n is the number of filters per octave.
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