Constant Q transform

In mathematics and signal processing, the constant-Q transform 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. In mathematics and signal processing, the constant-Q transform 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 logarithmically spaced filters fk, 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. The short-time Fourier transform of x for a frame shifted to sample m is calculated as follows: Given a data series sampled at fs = 1/T, T being the sampling period of our data, for each frequency bin we can define the following: