# Spatial Sound Rendering Using Intensity Impulse Response and Cardioid Masking Function
## 1 Introduction  
Sound engineering in post-production makes extensive use of the process of enhancing sound recordings with spatial aspects. This allows the listener to experience the acoustic properties of the space as intended by the sound engineer. Such a procedure aims to create a truly immersive experience for the listener with the appropriate listening equipment [1]. The spatialization of sound plays a vital role in virtual reality (VR) and augmented reality (AR) systems [2]. Many examples of the use of spatialized sound in the aforementioned technologies exist in the literature. The simplest method for positioning virtual sound sources in two-channel stereo is simple intensity panning. This method was generalized to 3D sound systems at the end of the last century by [PERSON] [3]. In [4], the authors used augmented reality with a unique role for sound and the direction of the apparent sound source in learning systems. Sound naturally results in increased immersion in both the VR and AR. The goal is to link sound to the real and virtual objects surrounding the user. Various methods, such as ray tracing, can be used to simulate the environment and its effects on sound propagation [5]. Other spatialization methods using simulated spatial room impulse responses together with a human directional perception model in the form of Head Related Transfer Function sets have been extensively studied by [PERSON] and [PERSON] [6; 7]. The methodology continues to improve, especially in terms of personalizing the HRTF response. A detailed small representation of the acoustic scene is also important in research on the hearing process, especially in combination with a visual representation of the scene [8], or, for example, in user evaluation in sound source localization tasks as one of the elements of the immersion degree of the system [9]. The issue of \"presence\" (understood as \"being there\") is one of the most relevant in terms of reproducing acoustic conditions that reflect the natural environment. In this regard, there are many studies on the individual elements of the acoustic scene in the context of VR ([10; 11]), as well as the interaction of vision and sound in the VR environment [12]. The above examples confirm the relevance of sound in the perception of both the real and virtual environments. Among the most significant factors in the spatialization of source audio material is their enrichment with artificial reverberation [13]. A standard solution that works well in practical conditions is convolution processors using room impulse responses. These responses are acquired in real objects or from modeling that considers room acoustics. Methods based on impulse responses recorded in real, mostly recognizable rooms allow for the best results given the current state of the art [14; 15]. Hence, the authors also undertook such a research direction. These impulse responses are usually recorded using at least two microphones in an appropriate arrangement and rooms with interesting acoustic properties, especially the reverberation. This method uses pseudorandom excitation (Maximum Length Sequence signal, MLS) or a sine sweep signal [16; 17]. The above-mentioned methods are well-known and widely used for stereo (two-channel) and surround (5.1) recordings. However, there is a constant search for better and more computationally efficient processing methods for immersive (3D) sound methods [18; 19]. The task of these systems is to improve the feeling of immersion in the sound environment. The systems themselves are characterized by a much larger number of speakers, which are placed in the horizontal plane surrounding the listener but also in planes parallel to it, both below and above the listener. A prerequisite for the detailed reconstruction of spatial immersions is the need to encode the audio signal and its spatial attributes so that the number of recorded channels coincides with the number of speakers.