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In this paper, we propose a novel algorithm to decode voltages from an analog voltage sensor. The first part of the paper demonstrates a theoretical framework that simplifies the analysis of voltages from a sensor. The second part details our proposed algorithm which is designed on top of the theory provided in the first part. Finally, we compare our method to state-of-the-art methods for decoding voltages using digital techniques such as Dynamic Least Squares and Extended Kalman Filter and show promising results by detecting up to 12 bits per sample even with slow sampling rates. The voltage from a sensor can be decoded if we deduce the following properties from the data:In order to infer these properties, we need to observe the voltage associated with one of the pixel's dark states, and map it to one of several modal frequencies. To learn these relationships, we use a supervised method: in general, we assume that pixels along one side (x-direction) of the line suffer sensed voltages in phase and/or amplitude while pixels on the other side face phase and/or amplitude inversion. By observing many sequences of black and white patches, we can learn relationships among different modal frequencies. In the following figure, we illustrate how these relationships can be inferred. In our approach, we model the four modes in a kind of "grid" structure. The pixel value in a given mode is a function of several pixel values around it: in addition to its own value in real space, the pixel in a certain mode depends on values at nearby pixels in both dimensions. We represent these dependencies in a directed acyclic graph (DAG). Figure 1 illustrates such an example where one pixel has three dependencies: its real-space value and the values at two neighboring pixels (Figure 1(a)). The DAG corresponding to this example is shown in figure 1(b). Once we have this kind of representation, the relationships between real-space values and sensed voltage values are straightforward to infer. Figure 2 shows three different paths from the "pixel" node of the DAG to one of its neighbors, each corresponding to a different modal frequency. For reference purposes, the actual voltages are plotted in figure 2 as well. Note that all three paths have similar amplitude but are out of phase with each other by about 90 degrees. We label the different paths using the modal frequency that they represent. Once these relationships are learned, one simply needs to transform real-space values to modal frequencies and apply the above transformation for each pixel. We employ two separate sensors with polarities reversed. If one sensor faces upward, so does the other sensor; if one faces left, so does the other one. The relationship between real-space values and sensed voltages can be inferred independently for both sensors by training them separately, and then combining the results of both sensors using a voting scheme. In this way we can detect up to 12 bits per sample even at slow sampling rates as low as 0.1 Hz with a non-optimal implementation of our method. eccc085e13
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