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Modeling and Delay-Equalizing Loudspeaker Responses

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This paper focuses on the modeling of the linear properties of loudspeakers. The impulse response of a generalized multi-way loudspeaker is modeled and delay-equalized using digital filters. The dominant features of a loudspeaker are its low- and high-frequency roll-off characteristics and its behavior at the crossover points. The proposed loudspeaker model also characterizes the main effects of the mass-compliance resonant system. The impulse response, its logarithm and spectrogram, and the magnitude and group-delay responses are visualized and compared with those measured from a high-quality two-way loudspeaker. The model explains the typical local group-delay variations and magnitude-response deviations from a flat response in the passband. The group-delay equalization of a three-way loudspeaker is demonstrated with three different methods. Time-alignment of the tweeter and midrange elements using a bulk delay is shown to cause ripple in the magnitude response. The frequency-sampling method for the design of an FIR group-delay equalizer is detailed and is used to flatten the group delay of the speaker model in both the whole and limited audio range. The full-band equalization is shown to lead to preringing in the impulse response. In contrast, group-delay equalization at mid- and high-frequencies only reduces the length of the loudspeaker impulse response without introducing preringing.

JAES Volume 66 Issue 11 pp. 922-934; November 2018
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AES - Audio Engineering Society