# Filter design by convex iteration

### From Wikimization

where

For low pass filter, the frequency domain specifications are:

To minimize the maximum magnitude of , the problem becomes

A new vector is defined as concatenation of time-shifted versions of , *i.e.*

Then is a positive semidefinite matrix of size with rank 1. Summing along each 2N-1 subdiagonals gives entries of the autocorrelation function of . In particular, the main diagonal holds squared entries of . Minimizing is equivalent to minimizing .

Using spectral factorization, an equivalent problem is