Quadrature mirror filter

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In digital signal processing, a quadrature mirror filter is a filter bank which splits an input signal into two bands which are subsampled by a factor of 2. The upper band has inverted frequencies, i.e. low frequencies are encoded as high frequencies and vice versa.

The filters <math>g[n]</math> and <math>h[n]</math> are related by the following formula:

<math>g[L - 1 - n] = ( - 1)^n \cdot h[n]</math>

where <math>0 \le n < L.</math>

Frequencies in the transition band are encoded in the low passed and the high passed band with different amplitudes.

Many of the common wavelets such as those constructed by Daubechies, Coifman, Mallat, etc. and their generating scaling functions satisfy a quadrature mirror filter relationship.es: Filtro espejo en cuadratura