## 6 From Single-Point to Multi-Point Equalization
### Prototype Approach  
The fuzzy c-means clustering approach of [70; 139] is also a first example of a _\"multi-point prototype approach\"_. These methods use measurements of the room response in different locations to extract a prototype response which is representative of the perceptual acoustic situation that has to be corrected. A single equalizer is then designed with indirect or direct methods [55], on the basis of this prototype response. Different approaches for the determination of the prototype response were studied in [144]. In particular, the fuzzy c-means method was compared with the mean average, the median, themin-max, and the root-mean-square average, and applied to fractional octave complex-smoothed spectra. The equalizer was then derived by inversion or the Kirkeby algorithm [81], or LPC analysis, with minimum-phase equalization. In the considered conditions, the mean average gave the best results, with the other methods also providing similar performance. The prototype extraction approach based on mean average was also combined with the method of [73] and applied to room-response equalization [75,145]. Subjective listening tests confirmed the good results obtained with the approach [75]. The approach was further extended in [146,147] by also considering a group-delay equalization. In [146], after the determination of the minimum-phase equalizer, the smoothed phase responses measured at different positions are corrected with the phase response of the equalizer and are used to determine the group delay responses. A prototype group delay is computed by averaging the group delay at the different positions, and after spectral smoothing is used to extract an all-pass FIR group-delay equalizer. In [147], the prototype phase response used to determine the phase equalizer is extracted only from the early reflections, which represent the contribution of the direct sound, discarding the late reflections that represent the reverberation of the environment. The mixing time between early and late reflections is calculated using the approach presented in [147,148] based on Gaussianity estimators. The prototype function is truncated using the mixing time, and an FIR phase equalizer is obtained with the matched filter technique; i.e., time-reversing the all-pass impulse response. With this approach, pre-ringing artifacts are avoided, since only the early reflections are considered in the equalizer. In fact, taking into consideration only the first reflections, only the main characteristics of the room are considered and those parts of the impulse response which contain zeros that vary with the position and according to [149] produce the pre-ringing artifacts are avoided. A prototype approach is also followed in [93,150,151,152,153]. According to the authors, _\"part of the impact of a listening room is natural to the human ear and should not be removed by a room correction system\"_[93]. In particular, sound reproduction in a room normally causes an increased sound pressure level at the lower frequencies, because of the lower absorption typically found at these frequencies. Since this effect is natural to the human ear, as it provides the sense of being in a room, room equalization systems should not be allowed to remove the smooth increase in level at low frequencies, also referred to as the _\"room gain\"_. The room gain describes how the room efficiency increases at low frequencies compared to high frequencies [152]. Moreover, the prototype response should preserve the basic characteristics of the loudspeaker; i.e., the equalizer should not try _\"to make all loudspeakers sound alike\"_. Thus, the developed system estimates the main characteristics of the loudspeaker: lower cut-off frequency and slope, sensitivity, directivity index, and upper cut-off for the treble driver. The equalizer is designed by acquiring information both of local properties at the listening position and on the acoustic power in the three-dimensional sound field.