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:

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.

The short-time Fourier transform of x[n] for a frame shifted to sample m is calculated as follows:

Given a data series at sampling frequency f_s = 1/T, T being the sampling period of our data, for each frequency bin we can define the following:

The equivalent transform kernel can be found by using the following substitutions:

After these modifications, we are left with

The variable-Q transform is the same as constant-Q transform, but the only difference is the filter Q is variable, hence the name variable-Q transform. The variable-Q transform is useful where time resolution on low frequencies is important^{[examples needed]}. There are ways to calculate the bandwidth of the VQT, one of them using equivalent rectangular bandwidth as a value for VQT bin's bandwidth.