Different Way To Same
Another way to consider off-axis listener positions is to determine the base equalization curve for the loudspeaker by observing its three-dimensional radiation balloon.
A properly gathered balloon will reveal the anechoic response of the loudspeaker at all listener angles.
Because the direct field of a loudspeaker is considered to be largely independent of the acoustic environment (at least at short wavelengths), direct field equalization based on balloon data has a strong theoretical basis.
Figure 1 (page 1) shows the axial frequency response of a multi-way loudspeaker. The dip in response at 2 kHz is due to phase cancellation between multiple drivers in the box.
A boost filter at this frequency center will restore the axial response to flat. Observation of the polars and the entire radiation balloon at 2 kHz (Figure 2 and 3, page 2) shows that even though they cancel on-axis, the devices come into phase at two off axis positions. At these angles there is most likely a significant peak in the response for many of the audience members.
The “correction” made to the on axis response will likely worsen the off-axis response where a greater number of listeners are located. Worse case is that one of the off-axis energy lobes covers a microphone position, so a boost filter will likely worsen the gain-before-feedback.
Devices that have a destructive phase offset at one listener position are likely to have an in-phase relationship at another. The on-axis notch might better be addressed by the use of precision signal delay between the elements to bring them into phase rather than feed them more energy.
What They Do
In general, the use of equalization will inflate or deflate the radiation balloon at a specified octave band. The same effect occurs at all angles around the device.
But what is often needed is a reshaping of the balloon. This can be accomplished by using multiple elements and varying their physical spacing and relative delay. This is the heart and soul of loudspeaker design.
Boost and dip filters applied based on the axial response only have a minimal affect on the balloon shape for those frequencies. A good loudspeaker design will direct the radiation lobes toward the audience.
For frequency bands where this is not happening due to phase interactions, precision signal delay can be used to steer the lobes to thedesired position.
Figure 2 and 3: The polars (above) and entire radiation balloon at 2 kHz. Even though they cancel on-axis, the devices come into phase at two off-axis positions.
It’s counterproductive to just pump more energy into the loudspeaker and increase the level for all listeners, which is exactly what an equalizer does. It should be noted that psychoacoustics also plays a role in this.
Peaks in a frequency response are much more audible (and bothersome) to humans than dips in the response. We’re more aware of “too much” than “too little.”
A safe approach to equalization that embodies the theories described here is to avoid the use of boost filters when calibrating a sound system since it’s better to have “too little” than to have “too much.”
By observing the axial response for equalization, and using cut-only filters to smooth the resonant peaks, acceptable results can likely be attained for most listeners, because off-axis lobes will not be “inflated” by the process. The balloon data of a loudspeaker can reveal what will happen off-axis if a boost filter is implemented to smooth the on-axis response.