Modeling and delay-equalizing loudspeaker responses

Aki Mäkivirta, Juho Liski, Vesa Välimäki

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
92 Downloads (Pure)


The impulse response of a generalized multi-way loudspeaker is modeled and is 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 characterizes also 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 in 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 the whole audio range and in a limited range. The full-band equalization is shown to lead to preringing in the impulse response. However, group-delay equalization at mid and high frequencies only reduces the length of the loudspeaker impulse response without introducing preringing.

Original languageEnglish
Pages (from-to)922-934
Number of pages13
JournalAES: Journal of the Audio Engineering Society
Issue number11
Publication statusPublished - 1 Nov 2018
MoE publication typeA1 Journal article-refereed

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