Measurement, Analysis, and Visualization of Directional Room Responses (2001)

Room impulse responses are inherently multidimensional, including components in three coordinate directions, each one further being described as a time-frequency representation. Suc h 5-dimensional data is di cult to visualize and interpret. We propose methods that apply 3-D microphone arrays, directional analysis of measured room responses, and visualization of data, yielding useful information about the time-frequency-direction properties of the responses. The applicability of the methods is demonstrated with three di erent cases of real measurements. INTRODUCTION A room impulse response, measured from a source to a receiver position, is inherently multidimensional. Traditionally, the evolution of an omnidirectional sound pressure response in a single point has been studied as a function of time and frequency. However, dividing the response further into directional components can reveal much more information about the actual propagation of sound in the room, as well as about its perceptual aspects. In this paper we propose methods that are based on 3-D microphone arrays, directional analysis of the measured responses, and visualization of such data in a way that yields maximal information about the time-frequency-direction properties of the response. MERIMAA ET AL. Measurement, Analysis, and Visualization of Directional Room Responses The measurement of directional room responses is made with a special 3-D microphone probe which basically consists of two intensity probes in each x-, y-, and z-coordinate directions and is constructed of small electret capsules. The responses are analyzed either with a uniform or an auditorily motivated time-frequency resolution. The analysis results in a significant amount of 5-dimensional data that is hard to visualize and interpret. Based on measured x/y/z-intensity components, intensity vectors (magnitude and direction) can be plotted in a spectrogram-like map, one vector for each time-frequency bin, illustrating the directional evolution of the field in time and frequency. Additionally, a pressure-related time-frequency spectrogram can be overlaid with the vectors, in gray levels or colors, illustrating for example a perceptually motivated spectrogram with no directional information. One such map can be used to illustrate the horizontal information and another one can be added for the elevation information. This technique is a part of a Matlab visualization toolbox for directional room responses developed by the authors, and it includes several other possibilities to analyze and represent room acoustical data. Traditional parameters and presentations are also available, some of them in 3-D versions, such as energy-time plots in desired directions. The paper starts with a discussion on measurements of directional room responses and sound intensity. This is followed by descriptions of the visualization method and the auditorily motivated time-frequency analysis. Finally, the applicability of the methods is demonstrated with three different cases of real measurements. DIRECTIONAL SOUND PRESSURE COMPONENTS Existing literature on room acoustics discusses mainly omnidirectional measurements with the exception of some special directional parameters. Directional room responses can be measured with either directional microphones or arrays of microphones. However, an array of omnidirectional microphones has some distinct advantages compared to directional microphones. Omnidirectional capsules can be made smaller and they usually behave more like ideal transducers. Further, if the omnidirectional signals are stored at the measurement time, it is possible to afterwards create varying directivity patterns based on a single measurement. Typical directivity patterns can be formed with an array of two or more closely spaced omnidirectional microphones and some equalization to compensate for the resulting non-flat magnitude response. For example the difference of two microphone signals gives a dipole pattern and adding an appropriate delay to one of the signals changes the pattern to a cardioid. Okubo et al. [1] have also proposed a method that uses a product of cardioid and dipole signals to achieve a directivity pattern more suitable for some directional room acoustics measurements. Various directional sound pressure responses can be used to plot traditional impulse responses, energy-time-curves or spectrograms that give information about the directional properties of the room responses. With larger microphone arrays it is also possible to form directivity patterns with very narrow beams and thus good spatial resolution. However, groups of similar plots for several different directions are not very visual or easy to interpret. Sound intensity as a vector quantity can solve some of the visualization problems in the method we are proposing in this paper. SOUND INTENSITY Sound intensity [2] describes the propagation of energy in a sound field. Instantaneous intensity vector is defined as the product of instantaneous sound pressure p(t) and particle velocity u(t) I(t) = p(t)u(t) (1) Based on the linearized fluid momentum equation, particle velocity in the direction n can be written in the form