Constant-Q transform

In mathematics and <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, the constant-Q transform and variable-Q transform, simply known as CQT and VQT, transforms a data series to the <a href="/facts/Frequency_domain/pyTVrUSq">frequency domain</a>. It is related to the <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a> and very closely related to the complex <a href="/facts/Morlet_wavelet/aTEPLUIM">Morlet wavelet</a> transform. Its design is suited for musical representation.

The transform can be thought of as a series of filters fk, logarithmically spaced in frequency, with the k-th filter having a <a href="/facts/Spectral_width/cPPAkubY">spectral width</a> 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 <a href="/facts/Octave_(electronics)/uGdI87T5">octave</a>.

Constant-Q transform open-in-new

Constant-Q transform