Detection of Constant Phase Shifts in Filters for Sound Field Synthesis

Filters with constant phase shift in conjunction with 3/6 dB amplitude decay per octave frequently occur in sound field synthesis and sound reinforcement applications. These ideal filters, known as (half) differentiators, exhibit zero group delay and 45/90 degree phase shift. It is well known that certain group delay distortions in electro-acoustic systems are audible for trained listeners and critical audio stimuli, such as transient, impulse-like and square wave signals. It is of interest if linear distortion by a constant phase shift is audible as well. For that, we conducted a series of ABX listening tests, diotically presenting non-phase shifted references against their treatments with different phase shifts. The experiments revealed that for the critical square waves, this can be clearly detected, which generally depends on the amount of constant phase. Here, -90 degree (Hilbert transform) is comparably easier to detect than other phase shifts. For castanets, lowpass filtered pink-noise and percussion the detection rate tends to guessing for most listeners, although trained listeners were able to discriminate treatments in the first two cases based on changed pitch, attack and roughness cues. Our results motivate to apply constant phase shift filters to ensure that also the most critical signals are technically reproduced as best as possible. In the paper, we furthermore give analytical expressions for discrete-time infinite impulse response of an arbitrary constant phase shifter and for practical filter design.