# A Biologically Inspired Sound Localisation System Using a Silicon Cochlea Pair
## 2 Materials and Methods
### Binaural CAR-FAC Pre-Processing  
The CAR-FAC cochlear model was proposed in Reference [37], and a real-time reconfigurable CAR-FAC implementation on FPGA was described in References [38; 39]. As shown in Figure 1A, the CAR models the basilar membrane (BM) function using a cascade of two-pole-two-zero resonators, \(H_{1}\) to \(H_{\text{N}}\). The poles of the two-pole-two-zero resonator are chosen to be equally spaced along the normalised length of the cochlea according to the Greenwood map function [40]. The FAC includes a digital outer hair cell (DIHC) model, a digital inner hair cell (DIHC) model, and combines local instantaneous nonlinearity with a multi-time-scale automatic gain control (AGC). In this work, to investigate the FAC effect on the system performance, we also use the CAR only as a linear cochlear pre-processing step to compare its performance with the CAR-FAC pre-processing. The details are described in the Results and Discussion section. The lateral inhibition (LI) function models the role of cochlear nucleus neurons. Here, we extend the work to implement a real-time binaural CAR-FAC system on an Altera Cyclone V FPGA board using time multiplexing and pipeline parallelising techniques, as shown in Figure 2. The detailed implementation of each element of the CAR-FAC and the LI is described in References [36; 38; 39; 41; 42]. In this work, the LI outputs from both 'ears' are used to generate correlogram in the Correlogram module, and the correlogram is the system output. Other choices for the output of the binaural CAR-FAC system include the BM and the DIHC. The CAR-FAC response forms the basis of this system, Figure 3 presents examples of a 70-channel CAR-FAC response to different input sounds. Figure 3A shows the BM response to a 500 Hz sine tone at six channels, and Figure 3B shows the BM spatial response across all the channels at time \(t\). At higher centre frequency (CF) channels, the 500 Hz waveform travels without significant gain, and the output shows a gradually increased gain across those channels. As the waveform reaches the 500 Hz CF channel, a maximum gain is shown. After this, the gain of the response reduces rapidly. Figure 3C shows the BM response of seven channels to a \"click\". The click is a short period broadband signal so that each channel effectively shows its impulse response, and the dominant response frequency corresponds to each channel's CF. Additionally, the response shows an increased gain in higher CF channels and a decreased gain in lower CF channels. Figure 3D shows the BM spatial response across all the channels at three times, \(t_{\text{o}}\), \(t_{1}\), and \(t_{2}\) (\(t_{\text{o}}<t_{1}<t_{2}\)). Figure 3E shows the BM response to a combined 200 Hz and 800 Hz sine wave at seven channels. At higher CF channels, the 200 Hz and 800 Hz are both visible. At the 800 Hz CF channel, the 800 Hz signal dominates. After this, the gain of the 800 Hz tone falls rapidly and only the 200 Hz tone response is left until the 200 Hz CF channel is reached. Figure 3F shows two strong response channels corresponding to 200 and 800 Hz across all the channels at time \(t\). Figure 1: Architecture of the binaural sound localisation system. (**A**) The Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) model, \(H_{1}\) to \(H_{\text{N}}\) are the transfer functions of the CAR part, the centre frequencies (CFs) of the resonators decrease from \(H_{1}\) to \(H_{\text{N}}\). The digital outer hair cell (DOHC), the digital inner hair cell (DIHC), and the automatic gain control (AGC) comprise the FAC part. The DIHC output is connected to the lateral inhibition (LI) function. (**B**) The LI unit; (**C**) The instantaneous correlogram: the circle marked with a cross is an instantaneous correlation unit, and the output from all the units forms a 2-D correlogram. (**D**) The onset detection function; (**E**) The onset correlogram; a short period after the onset detection, \(t_{\textbf{1}}\) to \(t_{n}\), includes \(n\) instantaneous correlograms.