All-pass digital filter design in the frequency-delay domain using the iterative quadratic maximum likelihood algorithm

A new domain, termed the frequency-delay is used to design stable, all-pass digital filters resembling a given delay response in the least-squares sense. This spectral technique identifies the delay response of a stable, second-order, all-pass digital filter as a double sideband suppressed carrier amplitude modulated signal in the frequency-delay domain. Iterative maximum likelihood techniques are used to render the filter coefficients. The algorithm is a significant improvement over related methods because it results in a physically realizable stable all-pass filter that closely approximates a desired delay response.