# Filter design by convex iteration

### From Wikimization

(Difference between revisions)

Line 5: | Line 5: | ||

For low pass filter, the frequency domain specifications are: | For low pass filter, the frequency domain specifications are: | ||

+ | |||

<math> | <math> | ||

\begin{array}{ll} | \begin{array}{ll} | ||

Line 24: | Line 25: | ||

A new vector <math>g \in \texttt{C}^\texttt{N*N} </math> is defined as concatenation of time-shifted versions of <math>h </math>, ''i.e.'' | A new vector <math>g \in \texttt{C}^\texttt{N*N} </math> is defined as concatenation of time-shifted versions of <math>h </math>, ''i.e.'' | ||

+ | |||

<math> | <math> | ||

g = \left[ | g = \left[ |

## Revision as of 17:19, 23 August 2010

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