The closed form error expression with Parseval's theorem

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Virginia Polytechnic Institute


The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters.

It is understood that the main reason to fail in the extension can be summarized as:

(1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system.

(2) The derivation procedure depends too much on cancellation among terms.

To compensate the above two points, an alternative method utilizing Parseval's theorem was presented.

The major problems in the extension of Yovit-Jackson's form are summarized as:

(1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression.

(2) To find mathematical relations between the original spectrum and factorized component spectra.

(3) To find the closed form expression of generalized transfer function of optimum operator.