by dr. peter d�antonio
In Part 4 (Surround Professional, December 2000), we discussed a new algorithm that can help minimize modal variations by determining the optimal room dimensions in a rectangular room. This program, called the Room Sizer, minimizes the standard deviation of a “fully excited” modal response, with the source in one trihedral corner and the listener in an opposite corner. Now not many people listen to surround sound using this configuration, but it does fully excite the modal response of the room and allow us to obtain the best room dimensions. Once we have built a dimensionally optimized room, what is the best listening configuration for the various surround formats? Where is the best listening “sweet spot” in the room? Where should you place your loudspeakers, keeping in mind that we now have five woofers and one or more subwoofers in a typical 5.1 configuration?
What you will experience is that the position of your listening position significantly determines what you hear, because you are coupling with the pressure variations in the room differently in different locations (see Part 1, SP, July 2000) and you are experiencing a different coherent interference between the loudspeaker and its immediate boundaries at each position (see Part 2, SP, August 2000). In fact, the difference between different listening positions/speaker locations can be more significant than the differences between different model loudspeakers1,2. You could have someone who owes you a favor move one of your speakers at a time around as you pass judgment on its position in a comfortable listening seat. The problem is that the speakers are correlated, and each depends on the position of the other, so this is not a good idea, plus, even if it were possible, you would spend a great deal of time doing it. Or, better yet, get a group of friends or employees to each position one of the speakers as you pass judgment on their location. This may have been possible for mono or stereo, but with the advent of 5.1 home theater and multichannel music, physical trial and error approaches become even less feasible. Why not let the “computer do the walking”? In Part 5 we discuss the second tool we have available to minimize acoustical distortion below roughly 300 Hz – speaker/listener placement.
Critical listeners have invested considerable time in trial and error attempts to minimize these effects, however, no automated method to search for the optimum locations has been proposed. The task of optimally locating five loudspeakers and multiple subwoofers presents a significant challenge. In addition to optimizing the low-frequency response via optimum listener/loudspeaker placement, one must also address imaging3,4 and the influence of acoustical surface treatment on the size and location of sonic images, as well as the sense of envelopment or spaciousness experienced in the listening room.
Therefore, to address these acoustical issues we describe an automatic computerized simulation program that suggests optimum locations for loudspeakers, listener, and acoustical surface treatment.
Optimization
Parts 1 and 2 describe the complex interaction among the listening room and the locations of the listener and loudspeakers. There are already guidelines and procedures available that address these issues5,6,7. Modal frequencies for cuboid rooms and their pressure distribution are well known8. These can be used to aid listener and loudspeaker placement and room design. Positioning loudspeakers different distances from the nearest floor and walls can reduce the speaker-boundary interference. Simple computer programs that simulate the effect of loudspeaker and listener placement are also available. While these procedures are useful, they can never properly account for the complex soundfield that occurs in real listening rooms. Optimum placement of the loudspeakers and listener must be made taking all of these factors into consideration simultaneously, since the speaker-boundary interference and modal excitation are independent effects. That is, listener/loudspeaker locations that minimize the speaker-boundary interference do not necessarily lead to minimum modal excitation, and vice versa. To my knowledge, such an algorithm has not been published. For this reason, an iterative image method was developed to optimize the placement of listener and loudspeakers by monitoring the combined standard deviation of the speaker-boundary interference and modal response spectra.
In recent years, there has been a great increase in knowledge concerning computer models to predict the acoustics of enclosed spaces9. In addition, there has been a great increase in the computing power available on personal computers. This enables algorithms, which determine the best listener and loudspeaker position within a space, to use complex calculation procedures based on more accurate predictions of the soundfield received by the listener. These have many advantages over the simpler placement theories. For example, they take into account many more reflections from all surfaces in the room. This enables the examination of the subtle effects of many surfaces working in unison. Furthermore, by combining the room prediction models with optimization routines, the computer can determine the best positions for the loudspeakers and listener by processing the laborious trial-and-error optimization rather than the user.
In this discussion, a program is described that combines an image source model to calculate the room transfer function with a simplex routine to carry out the optimization process. An appropriate cost function (metric or measure) to characterize the quality of the spectra received by the listener has been developed. This parameter is based on the extensive subjective evaluations and listening tests of Toole and his colleagues10,11,12,13. They have confirmed that speakers that have flat on-axis frequency responses are preferred in standardized listening tests. In addition, similarly good off-axis response is also required, since the listener is hearing the combination of direct and reflected sound from the room’s boundary surfaces. At low frequencies, speakers are essentially omnidirectional. Since most rooms are not anechoic at low frequencies, we have chosen the flatness of the perceived spectra as a way to evaluate listener and loudspeaker placement. The “cost” parameter penalizes positions with uneven spectral responses. The optimization program we describe concentrates on lower frequencies (
