![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/CQT-piano-chord.png/640px-CQT-piano-chord.png&w=640&q=50)
Constant-Q transform
Short-time Fourier transform with variable resolution / From Wikipedia, the free encyclopedia
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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[1] and very closely related to the complex Morlet wavelet transform.[2] Its design is suited for musical representation.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/CQT-piano-chord.png/640px-CQT-piano-chord.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/C-major-piano-chord-waveform.png/640px-C-major-piano-chord-waveform.png)
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:
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.