# Spatial Sound Rendering Using Intensity Impulse Response and Cardioid Masking Function
## 2 Idea of the Proposed Method and General Algorithm  
The proposed method assumes recording the pressure impulse response with a pressure microphone of relatively high quality, characterized by the flatter amplitude frequency response and better phase frequency response over the entire audible acoustic bandwidth compared to directional microphones. This omnidirectional impulse response in the next stage is used to obtain an arbitrary set of impulse responses. This is the basis for obtaining professional final sound effects of recordings and rendering. As a bonus, it guarantees the full compatibility of the resulting surround sound with the mono signal, which is still essential for broadcasting systems. Impulse responses for individual channels require information regarding the direction of propagation of the sound wave reaching the omnidirectional microphone obtained from the second sensor, a 2D or 3D intensity probe. The registration of signals in both sensors is performed simultaneously, guaranteeing a high level of synchronization of the two sets of data. Measuring the sound intensity generated by acoustic sources is not a trivial task. Professional measuring instruments are used to make sound intensity measurements. The market offers specialized probes of both types: pressure-pressure (e.g., Bruel& Kjaer, GRAS) and pressure-velocity (e.g., Microflown, Weles Acoustics). Such measurement instruments are not widespread in the broader music recording and multimedia production communities primarily because of the cost and difficulty of the measurement process itself. However, it is possible to use the so-called mechatronic probe described by the authors in [22, 23]. This solution makes it possible to obtain the required impulse responses, does not require the use of expensive specialized sensors, and makes it possible to record the intensity response to a known excitation signal, which corresponds to measurements of the room's impulse response. According to the concept of the mechatronic pressure-pressure probe, one pressure microphone can be used to measure the intensity response by placing it sequentially in four (2D) or six (3D) mutually perpendicular measurement positions approximately 10 mm apart. This involves placing the microphones in two positions along the x- and y-axes and possibly the z-axis, respectively. The idea of the mechatronic probe for one axis is illustrated in Figure 1.  
Thus, the starting point of the proposed method is the recording of the pressure impulse and directional intensity responses. Examples of visualizations of such signals are shown in Figures 2-4. In Figure 2, we observe the classical impulse response as the signal amplitude as a function of time. Figure 3 shows the directional intensity response, where successive time instants are assigned to a sound intensity vector. The progression of time is visualized using a color scale. A better visualization of the evolution of the amplitude and direction of sound propagation in 2D is shown in Figure 4, where the z-axis represents time. It should be noted that the sound field in a closed room, particularly away from the source, is characterized by a high level of dispersion. This indicates that sound intensity has both active and reactive components. Choosing the integration (averaging) time of instantaneous intensity values is necessary to properly determine the active components associated with the propagation of direct sound and first reflections. The optimal time was found to be related to the perceptual properties of human hearing, and based on preliminary tests, it was determined to be 12 ms, which is a value related to the boundary delay in echo perception (Haas effect).