In digital signal processing, a quadrature mirror filter is a filter most commonly used to implement a filter bank that splits an input signal into two bands. The resulting high-pass and low-pass signals are often reduced by a factor of 2, giving a critically sampled two-channel representation of the original signal.
The analysis filters are related by the following formulae:
where is the frequency, and the sampling rate is normalized to .
In other words, the power sum of the high-pass and low-pass filters is equal to 1. The filter responses are symmetric about
Orthogonal wavelets -- the Haar wavelets and related Daubechies wavelets, Coiflets, and some developed by Mallat, are generated by scaling functions which, with the wavelet, satisfy a quadrature mirror filter relationship.
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