Adjoint filter


Adjoint filter

In signal processing, the adjoint filter mask h^*of a filter mask his 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 the sequenceswith respect to the Euclidean norm.:langle h*x, y angle = langle x, h^* * y angle

The autocorrelation of a signal xcan be written as x^* * x.

Properties

* {h^*}^* = h
* (h*g)^* = h^* * g^*
* (hleftarrow k)^* = h^* ightarrow k


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