Time-Alignment of Multi-Way Speakers with Group Delay Equalization - I
In this paper, a first of two-parts, a technique for time-aligning the driver responses (viz., woofer, mid-range, and tweeter responses) in a multi-way speaker system is presented. Generally, woofers exhibit a much larger time-of-arrival delay, at a listening position, compared to the mid-range and high-frequency drivers. Moreover, the time-of-arrival delay for all drivers is frequency dependent exhibiting a large variation over the audible frequency domain. Due to these differences, a two-part study was undertaken to understand the effects of these variations, quantitatively and qualitatively. In this first part, we present the motivation behind the system used for applying all-pass filters to process audio signals being delivered to the multi-way speaker and propose a time-delay difference equalization technique. We show that applying all-pass filters result in significant ``temporal-smearing' of the response, despite flattening of the group delay response. Thus depending on the amount of group-delay equalization, the smearing with pre-ring effects could potentially have audible effects depending on the content. However, despite the temporal-smearing (viz., response-dilation in time) for an arbitrary-order all-pass filter, we show that the time-frequency characteristics of these group-delay equalizing filters exhibit a uniform decay rate at all-frequencies allowing group-delay equalization without affecting the modal decay rates. Thus this enables other cascaded filter structures to be utilized for modal equalization in additional to conventional loudspeaker-room equalizers. We also propose group-delay flattening for the woofer and a small range of the midrange frequencies through a weighted approach at the lower frequencies for group-delay equalization. Future work will involve investigations using perceptually motivated variable-octave complex smoothing of responses (1/24-th octave smoothing at low frequencies and 1/3-rd octave at higher frequencies), and designing all-pass filters based on this phase-smoothed data. Quantitative results obtained will be presented in this paper, whereas the next part of the two-part paper will present results from listening tests.
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