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.
Frequencies in the transition band are encoded in the low passed and the high passed band with different amplitudes.
It is interesting to note that 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.