The design of all-pass filters as delay distortion compensators: Eigenfilter and delay-spectrum design techniques

Phase distortion correction finds applications in diverse fields from image processing to multirate digital filtering. Several attractive techniques for phase compensation have been developed. Some techniques calculate digital filter coefficients from a given set of constraints on the filter amplitude and phase characteristics. Often this method yields a mathematically sound solution, but an unstable filter. Others design methods require a precise initial guess. All current phase compensation design techniques employ digital all-pass filters to achieve the desired phase or delay correction. This thesis explores alternate techniques to design all-pass digital filters in phase or delay compensation problems.; All-pass digital filters are used for phase/delay compensation because they do not introduce amplitude distortion as Finite Impulse Response (FIR) or Infinite Impulse Response (IIR) filters may do. However, there is no well-established method for all-pass digital filter design. We begin by investigating the eigenfilter method for phase equalization. We then derive an enhanced eigenfilter algorithm that improves convergence for low order digital filter design. A delay equalization algorithm that uses cascaded second-order all-pass digital filters is next proposed. In this technique, each filter's delay is uniquely characterized by only two parameters. Appropriate selection of these parameters ensures a causal, stable filter realization.; This thesis also introduces a novel design method whereby a given delay function is transformed into a time-delay domain. Applying spectrum estimation techniques, the all-pass digital filter parameters of each filter can be identified, along with the number of times each filter is used. This multiplicity on the filters introduces the need for fractional delay, a concept that is investigated and later used in the search for an optimal solution. A filter optimization, based on a genetic algorithm, finds the coefficients for each second-order all-pass digital filter. Design examples support the theoretical development, and mean squared error performance metrics are used to evaluate the design techniques.