Modeling and delay-equalizing loudspeaker responses

Abstract

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.