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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“Customs and convictions change; respectable people are the last to know, or to admit, the change, and the ones most offended by fresh reflections of the facts in the mirror of art.”
—John Updike (b. 1932)