ROW NORMALIZED PEF

row normalized PEF We often run into bursty noise. This can overwhelm the estimate of a prediction-error filter. To overcome this problem we can use a weighting function. The weight for each row in fitting matrix () is adjusted so that each row has about the same contribution as each other row. A first idea is that the weight for the n-th row would be the inverse of the sum of the absolute values of the row. This is easy to compute: First make a vector the size of the PEF $\bold a$ but with each element unity. Second, take a copy of the signal vector $\bold y$but with the absolute value of each component. Third, convolve the two.

The convolution of the ones with the absolute values could be the inverse of the weighting function we seek. However, any time we are forming an inverse we need to think about the possibility of dividing by zero, how it could arise, and how divisions by ``near zero'' could be even worse (because a poor result is not immediately recognized). Perhaps we should use something between $\ell^1$ and $\ell^2$ or Cauchy. In any case, we must choose a scaling parameter that separates ``average'' rows from unusually large ones. For this choice in subroutine rnpef1(), I chose the median.