Editing Adaptive filter (section)

===Adaptive Linear Combiner===

:[[File:Adaptive Linear Combiner General.png|thumb|400px|alt=A block diagram of an adaptive linear combiner with a separate block for the adaptation process.|Adaptive linear combiner showing the combiner and the adaption process. k = sample number, n=input variable index, x = reference inputs, d = desired input, W = set of filter coefficients, ε = error output, Σ = summation, upper box=linear combiner, lower box=adaption algorithm.]]   [[File:Adaptive Linear Combiner Compact.png|thumb|400px|alt=A compact block diagram of an adaptive linear combiner without a separate block for the adaptation process.|Adaptive linear combiner, compact representation. k = sample number, n=input variable index, x = reference inputs, d = desired input, ε = error output, Σ = summation.]]

The adaptive linear combiner (ALC) resembles the adaptive tapped delay line FIR filter except that there is no assumed relationship between the X values. If the X values were from the outputs of a tapped delay line, then the combination of tapped delay line and ALC would comprise an adaptive filter. However, the X values could be the values of an array of pixels. Or they could be the outputs of multiple tapped delay lines. The ALC finds use as an adaptive beam former for arrays of hydrophones or antennas.

:<math> y_k= \sum_{l=0}^L w_{lk} \ x_{lk} = \mathbf{W}_k^T \mathbf{x}_k  </math>  
::where <math> w_{lk}  </math> refers to the <math>l</math>'th weight at k'th time.