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.

Embodiment disclosed herein enable detection and improvement of the quality of the audio signal using a mobile device by determining the loss in the audio signal and enhancing audio by streaming the remainder portion of audio. Embodiments disclosed herein enable an improvement in the sound quality rendered by rendering devices by emitting an test audio signal from the source device, measuring the test audio signal using microphones, detecting variation in the frequency response, loudness and timing characteristics using impulse responses and correcting for them. Embodiments disclosed herein also compensate for the noise in the acoustic space by determining the reverberation and ambient noise levels and their frequency characteristics and changing the digital filters and volumes of the source signal to compensate for the varying noise levels.