Further results on the WLS design of variable fractional delay filters

The weighted least-squares design of Farrow-based variable fractional delay filters is known to suffer from numerical difficulties which can lead to design failures. In this paper, we derive a set of analytical expressions to overcome these difficulties. The analytical expressions also allow us to prove conclusively a number of properties that previous researchers have claimed regarding the design of variable fractional delay filters. We also unify under a common framework the various weighted least-squares design formulations that have been proposed and studied.