# Project3 - ECE 5650/4650 Computer Project #3 Adaptive...

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Background Theory 2 (3) The solution is a result of the projection theorem or orthogonality principle 1 , which says that we choose constants such that the error is orthogonal to the observations ( data ), i.e., (4) The resulting system of equations (5) are known as the normal equations , or in Papoulis the Yule-Walker equations. The function is the autocorrelation sequence corresponding to and is the cross correla- tion sequence between and . In an adaptive Wiener filter the error signal is fed back to the filter weights to adjust them using a steepest-descent algorithm . Note that the error surface generated by over the parameter space is convex cup (i.e. a bowl shape) as shown in Figure 2. The filter decorrelates the output error so that signals in common to both and in a correla- tion sense are cancelled. A block diagram of an adaptive FIR filter is shown in Figure 3.
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Project3 - ECE 5650/4650 Computer Project #3 Adaptive...

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