# A Comparison between Horizontal and Vertical Interchannel Decorrelation
## 1 Introduction  
It is well documented in the literature that horizontal interchannel decorrelation between left and right loudspeaker signals relates directly to the perceived width of the horizontal auditory image [1]. This is due to a strong relationship between the interchannel cross-correlation (ICC) and interaural cross-correlation (IAC)--it is known that the IAC coefficient (IACC) is a good indicator of apparent source width (ASW) in concert hall acoustics, as dictated by decorrelated early reflections from lateral directions [2]. In turn, an artificial synthesis of this natural decorrelation controls the horizontal extent of a phantom auditory image between left and right loudspeaker channels. A visual representation of this can be seen on the left of Figure 1 below, where the phantom auditory image of the ICCC 1.0 condition (full correlation between the two loudspeaker signals) is narrow and located directly between the two source positions--decorrelation of the two signals then extends the horizontal image spread (HIS) towards the locations of the loudspeakers. In contrast, very little is known about the psychoacoustic effects of interchannel decorrelation in the vertical domain. Research regarding vertical panning demonstrates that an elevated phantom image is generated between two spaced coherent signals (as represented by the ICCC 1.0 image on the right of Figure 1) [3, 4, 5]. However, there has been little investigation into how this phantom image is perceived when the correlation between the two signals is decreased. If the perception of vertical decorrelation were similar to that of horizontal decorrelation, then a decrease of correlation would result in an increase of vertical image spread (VIS) (as proposed in Figure 1), possibly mimicking the effect of decorrelated ceiling re actions--it has previously been suggested that a single ceiling re action can increase the perception of VIS [6, 7]. This comparison between horizontal and vertical decorrelation is the focus of the current experiment, where both domains are judged using the same stimuli and under the same testing conditions. Taking into account the perceptual cues of vertical localisation, frequencies above around 3 kHz are important for elevation perception [8, 9]; it could therefore be considered that any effect of vertical decorrelation might be frequency-dependent as well, potentially with a greater in uncence from the key high frequency regions related to vertical localisation. In order to observe the spectral impact alone, the current study assesses the effect of vertical decorrelation in the median plane where there is little interaural difference, except for that caused by ear asymmetry at high frequencies [10]. Considering the above background, the following research questions are proposed:  
Is there a direct relationship between vertical ICC and VIS in the median plane? How does vertical decorrelation compare to horizontal decorrelation? Is the perception of horizontal and vertical decorrelation frequency-dependent? In order to answer the above questions, broadband pink noise has been filtered into three frequency bands: 'Low' (octave-bands with centre frequencies of 63-250 Hz), 'Middle' (centre frequencies of 0.5-2 kHz) and 'High' (centre frequencies of 4-16 kHz). These three frequency bands were each decorrelated with varying degrees of ICC and presented in multiple comparison trials (both horizontally and vertically), to observe whether an ICC effect is apparent for the different groups of frequencies. Two subjective listening tests were conducted to grade the perceived magnitudes of HIS and VIS for the stimuli with different frequency bands and ICCs. Preliminary results of the tests were presented in [11]. The current paper describes the experimental design in detail and provides complete statistical analyses of the data obtained. Furthermore, various objective measurements are carried out on the binaural recordings  
Figure 1: Visualisation of horizontal and (potential) vertical interchannel decorrelation perception.