## 1 Introduction  
Auralization is a subject of great interest in different areas because it enables the generation of an audible perception of the acoustic properties of a specific environment [1]. It is a powerful technique because it allows the sound field to be rendered according to the characteristics of the medium, which has applications in the evaluation and understanding of the physical phenomenon under consideration. For room acoustics, auralization provides a convenient tool for experimental tests, subjective evaluations, virtual reality and architectural design. A significant feature that enhances the auralization technique is the generation of interactive environments in which the listener can move within the enclosure. This is achieved by synthesizing the acoustic field in real time according to the properties of the room and the source-receiver paths. Several approaches have been proposed in the scientific literature to generate interactive auralizations based on Geometrical Acoustics (GA) [2; 3; 4; 5; 6]. Nevertheless, at low frequencies, the assumptions required for GA are not generally satisfied, which requires the use of different techniques, such as the numerical solution of the wave equation. The Finite Element Method (FEM) [7], the Boundary Element Method (BEM) [8] and the Finite Difference Time Domain (FDTD) method [9] are some of the techniques commonly used to estimate room impulse responses. However, the computational cost required by these approaches to predict the solution constrains their use for real-time applications. Despite the significant computational cost of the above methods, some alternatives have been formulated to generate interactive environments based on wave propagation. [PERSON] et al. proposed the use of the equivalent source method for the rendering of acoustic fields of large and open scenes in real time [PERSON] et al. (2010). Although the approach allows for the reconstruction of the sound field in real time, limitations related to static sound sources or the inclusion of the Doppler effect have to be overcome. The inclusion of the directivity of sound sources and listeners using a spherical harmonic representation has also been proposed by the same author to extend the versatility of the methodology [PERSON] et al. (2010). Another approach proposed by [PERSON] (2012) simulates the synthesis and propagation of sound. The solution method, denoted as Adaptive Rectangular Decomposition (ARD), permits real-time computation providing a platform for interactive auralizations. The main advantages of the method are the use of dynamic listener/sources and its ability to simulate large complex 3D scenes. Alternatively, [PERSON] presented a different strategy to predict acoustic fields in real time [PERSON] (2013). The numerical solver corresponds to an FDTD model running over GPUs using parallel computing techniques. The results indicate that this methodology allows the simulation up to 1.5 kHz in moderate size domains. Dynamic listener and multiple sources are also possible based on this processing scheme. A different approach to interactive auralizations based on the numerical solution of the wave equation is to encode spatial information from the predicted acoustic pressure data. Translation and rotation of the acoustic field can be then achieved by the application of mathematical operators. [PERSON] et al. [PERSON] et al. (2014) proposed a method to obtain a spherical harmonic representation of FDTD simulations. The approach uses the the Blumlein difference technique to create a higher order directivity pattern from two adjacent lower orders. This is achieved by approximating the gradient of the pressure as the difference between two neighbouring pressure points on the grid where the solution was computed. The rotation of the acoustic field can be easily computed by a rotation matrix, whereas the translation can be recreated by an interpolation process between spatial impulse responses [PERSON] et al. (2016). [PERSON] et al.