# Predicting the Colouration between Binaural Signals
## 3 Validation
### Listening Test
#### 3.2.1 Test Paradigm  
The listening test followed the MUSHRA paradigm, ITU-R BS.1534-3 [47], using webMUSHRA [48] ([[https://github.com/audiolabs/webMUSHRA](https://github.com/audiolabs/webMUSHRA)]([https://github.com/audiolabs/webMUSHRA](https://github.com/audiolabs/webMUSHRA)), accessed 16 December 2021). The base stimulus was one second of monophonic pink noise at a sample rate of 48 kHz, windowed by onset and offset half-Hanning ramps of 5 ms. Each test sound was first generated by convolving the pink noise with HRTFs from the Bernschutz Neumann  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **1 kHz** & **5.5 kHz** \\ \hline BSD (dB) & 0.15 & 0.15 \\ PEAQ (ODG) & 1.08 & 0.27 \\ CLL (Phons) & 0.50 & 0.15 \\ PBC (sones) & 0.91 & 0.12 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculated colouration values between 1 kHz and 5.5 kHz +20 dB peak filtered signals with 100 Hz \(-\)3 dB filter bandwidths and flat response signals of the same level.  
Figure 9: Frequency response of the 1 kHz (blue line) and 5.5 kHz (red line) +20 dB peak filters of 100 Hz \(-\)3 dB filter bandwidths, used to assess the use of equivalent rectangular bandwidth (ERB) weighting, for which a 100 Hz bandwidth peak at a lower frequency should be weighted greater.  
KU 100 database [49]. The test sound locations (\(\psi\)) of the HRTFs corresponded to the central points of the faces of a dodecahedron. To reduce the total number of trials, symmetry was assumed and thus only locations in the left hemisphere were used, amounting to 8 locations (see Table 5). All binaural renders were static (fixed head orientation) to ensure consistency in the experience between participants. Low anchor and medium anchors were low-pass filtered versions of the reference with an \(f_{c}\) of 3.5 kHz and 7 kHz, respectively.  
For each test sound location, the conditions were degraded versions of the reference created using a 10-band filter stage in one octave bandwidths from 31.5 Hz to 16 kHz, with centre and edge band frequencies as in the ANSI standard S1.11-2004. The gain of each octave band filter was calculated as \(Rg_{\text{EQ}}\), where \(R\) is a uniformly distributed random number that follows \(R=\mathbb{R}\), \(R\in(-0.5,0.5)\), and \(g_{\text{EQ}}\) is the equaliser gain. Filters were generated separately for left and right ears in order to increase the binaural differences between conditions, such that some conditions would have larger gains in certain frequency bands in the ipsilateral signal, and some in the contralateral. For each test sound location, seven test conditions were generated using equaliser gains \(g_{\text{EQ}}=\{1,2,4,6,8,12,16\}\), totalling 7 conditions per test sound location, and therefore 56 in total. An illustration of the 10-band equaliser with varying equaliser gains (for one ear) is presented in Figure 10. Equaliser curves were applied to the binaural pink noise signals.  
For each trial, the listener was asked to rate the stimuli in terms of similarity to the reference. The presentation of stimuli and trials was randomised and double blind, and participants were able to adjust the playback level at the start of the test, after which it was fixed.