- Adjoint filter
In

signal processing , the**adjoint filter mask**$h^*$of a filter mask $h$is reversed in time and the elements are complex conjugated.:$(h^*)\_k\; =\; overline\{h\_\{-k$Its name is derived from the fact, that the convolution with the adjoint filteris the adjoint operator of the original filterwith respect to the

Hilbert space $ell\_2$ of thesequence swith respect to theEuclidean norm .:$langle\; h*x,\; y\; angle\; =\; langle\; x,\; h^*\; *\; y\; angle$The

autocorrelation of a signal $x$can be written as $x^*\; *\; x$.**Properties*** $\{h^*\}^*\; =\; h$

* $(h*g)^*\; =\; h^*\; *\; g^*$

* $(hleftarrow\; k)^*\; =\; h^*\; ightarrow\; k$

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