## 2 Methodology
### Recording Audio Data  
During the recording session, dual on-board microphones located near the top and bottom of the device (see Figure 2) are used to record the stereo microphone input, captured at 44.1 kHz sampling rate in 16-bit pulse-code modulation (PCM) format. Interactions with the touchscreen create a mechano-acoustic response presenting as an impulse in the continuous microphone signal as shown in Figure 3. We record and label touch inputs for each location (Top-Left, Mid-Right etc.) in separate sessions to create the corresponding training and test datasets. Figure 3 shows the signal from the top and bottom microphones are out of phase, alluding to the opposite orientation of the microphone membranes receiving the pulse which distinguishes the two signals. The difference between the amplitude of the pulse hints at the different degrees of mechanical coupling and internal gain of the two microphones. The difference in amplitude in the signals could be attributed to the proximity of one microphone to the source of the pulse compared to the other. We further note that the initial transient in the top signal contains a sharp spike absent from the bottom signal while a larger difference is observed between the first maxima and minima of the bottom signal. The bottom signal also has a longer tail with more oscillations after the pulse while top signal fall away quickly. With a single microphone signal, the pulse generated from a tap contains information about the touch input location based on how the sound waves propagate through the device, with different locations causing the phone to vibrate and respond uniquely (the phone's interior structure is not homogeneous). The fact that pulses observed in the top and bottom signals do not simply reflect each other suggests that the signal received at the two microphones are in fact unique. Furthermore, aftershocks with multiple peaks reflect the complex interactions between the finger and mechanical response of the phone which could include internal mechanical reflections. These repeated  
Figure 2: Device microphone locations. Note that the microphone placement deviates from the central axis and is position asymmetrically on the top and bottom of the device. peaks, may have unique magnitudes and time intervals associated with the location of the touch input as listened from two microphones positioned asymmetrically on the device. From these observations, we posit that the top and bottom microphones hear a different acoustic signal, distinguishable in their response from the same pulse which supports our assumption of uniqueness of the two signals. Our approach hinges on the uniqueness of the response of each microphone but it is the systematic difference between the two that allows our machine learning model to distinguish the location of the touch input. To identify and isolate the segments of acoustic signal that correlate with touch input location, we apply smoothing (moving average of 11 samples) before peak detection on the acoustic recording as seen in Figure 4, to ensure impulse-like signals are detected. A local peak detection algorithm is applied with a sliding window to select the local maximum element from the neighbourhood of the chosen frame. These detected peaks are compared against the entries from a local minimum detection algorithm applied on the original signal to exclude areas of elevated signal which are non-impulsive (plateaus) from our peak detection dataset. We apply an empirically determined peak window size of 5 k samples points (110 ms) and peak intensity threshold of 20% determined empirically. Figure 3: Typical acoustic waveform from tapping the Mid-Left location: Top waveform—Top microphone (blue), Bottom microphone (red). Every tick on the horizontal axis is 10 milliseconds. Acoustic features commonly used in audio recognition and audio classification problems were extracted using an Open-Source Python Library for acoustic Signal Analysis pyAudioanalysis [20].