Remez Exchange Algorithm and it's Flowchart|| Info You

 Remez Exchange Algorithm 

The Remez algorithm sometimes called as Remes algorithm. This algorithm is published by Evgeny Yakovlevich Remiz. It is a highly effective iterative procedure, that is used to determie the location of the external frequency.

It consists of the following steps at each stage of iteration.

Step-1:

A set of initial values for external frequencies are either chosen or are available from the completion of the previous iteration.

Step-2:

The value of e is computed by solving the matrix shown below, resulting the expression

Where the constant Cn is given by

Step-3:

The value of the amplitude response A(w) at W = Wi are then computed using

Step-4:

The polynomial A(w) is determined by interpolating the above values at L+2 external Frequencies using the Lagrange interpolation formula.

Where

Step-5:

The new weighted error function e(w) is computed at a dense set S(S>=L) of frequencies. 

Step- 6:

If the peak value e of e(w)are equal in magnitude, The algorithm has converged. 

Else go back to step 2.

Flowchart of Remiz Exchange Algorithm

Figure. Flowchart of Remez exchange algorithm