Adjoint filter

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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 filter is the adjoint operator of the original filter with respect to the Hilbert space \ell_2 of the sequences with respect to the Euclidean norm.

\langle h*x, y \rangle = \langle x, h^* * y \rangle

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


  • {h^*}^* = h
  • (h*g)^* = h^* * g^*
  • (h\leftarrow k)^* = h^* \rightarrow k