A high performance, low complexity phase shift network may be created with one or more non-first-order all-pass recursive filters that are built on top of a plurality of first-order and/or second-order all-pass recursive filters and/or delay lines. A target time delay, whether large or small, may be specified as a constraint for a non-first-order all-pass recursive filter. A target phase response may be determined for the non-first-order all-pass recursive filter. Phase errors between the target phase response and a calculated phase response with filter coefficients of the non-first-order all-pass recursive filter may be minimized to yield a set of optimized values for the filter coefficients of the non-first-order all-pass recursive filter.