Adjoint filter

From Wikipedia, the free encyclopedia

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.

[edit] Properties

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