常数Q变换

常数Q变换（英语：Constant Q transform）是数学和信号处理中的变换，将数据变换到频域内。它与傅里叶变换相关^[1]，而且与莫莱小波变换紧密相关^[2]。

常数Q变换可以视为是许多对数分布滤波器的组合，其中第k个滤波器其带宽是上一个滤波器带宽的某个倍数，也就是

${\begin{aligned}\delta f_{k}&=2^{\frac {1}{n}}*\delta f_{k-1}\\&=\left({2^{\frac {1}{n}}}\right)^{k}*\delta f_{\mathrm {min} }\end{aligned}}$

其中

δf_k为第k个滤波器的带宽

f_min为最低滤波器的中心频率

n 为每个Octave的滤波器数

参考资料

^ Judith C. Brown, Calculation of a constant Q spectral transform （页面存档备份，存于互联网档案馆）, J. Acoust. Soc. Am., 89(1):425–434, 1991.
^ Continuous Wavelet Transform （页面存档备份，存于互联网档案馆） "When the mother wavelet can be interpreted as a windowed sinusoid (such as the Morlet wavelet), the wavelet transform can be interpreted as a constant-Q Fourier transform. Before the theory of wavelets, constant-Q Fourier transforms (such as obtained from a classic third-octave filter bank) were not easy to invert, because the basis signals were not orthogonal."