Van Citteri's Iteration (1931)

In the Fourier domain, the following identity must hold for all

Applying making successive substitutions,

Enumerating

If , then

which is the inverse filter solution. This iteration retains many of disadvantages of the inverse filter operation, but

• It can be terminated prior to convergence
• The inverse operator does not need to be built

For this iteration to converge, we need , or equivalently

which is a disk of radius 1 centered at (1,0) in the complex plane with axes and .

For real-valued and ,

The final condition is a common necessary condition for convergence in iterative linear systems, e.g. adaptive LMS FIR filters.