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 in which the inner product is 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 .
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 in which the inner product is 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 .
Properties
{h^*}^* = h (h*g)^* = h^* * g^* (h\leftarrow k)^* = h^* \rightarrow k
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