Abstract
Time-encoding circuits operate in an asynchronous mode and thus are very suitable for ultra-wideband applications. However, this asynchronous mode leads to nonuniform sampling that requires computationally complex decoding algorithms to recover the input signals. In the encoding and decoding process, many non-idealities in circuits and the computing system can affect the final signal recovery. In this article, the sources of the distortion are analyzed for proper parameter setting. In the analysis, the decoding problem is generalized as a function approximation problem. The characteristics of the bases used in existing algorithms are examined. These bases typically require long time support to reach good frequency property. Long time support not only increases computation complexity, but also increases approximation error when the signal is reconstructed through short patches. Hence, a new approximation basis, the Gaussian basis, which is more compact both in time and frequency domain, is proposed. The reconstruction results from different bases under different parameter settings are compared.
Highlights
Time encoding is an asynchronous process for mapping the amplitude information of a band-limited signal x(t) into a sequence of strictly increasing time points
Non-ideality analysis in certain theoretical cases, the signal sampled through time-encoding machine (TEM) can be perfectly recovered, in all practical applications, there are multiple non-idealities that lead to reconstruction errors both in the encoding and in the decoding processes
Large entries from division operation in solving the Vandermonde system may still amplify the quantization noise contained in the measurements
Summary
Time encoding is an asynchronous process for mapping the amplitude information of a band-limited signal x(t) into a sequence of strictly increasing time points (tk). Non-ideality analysis in certain theoretical cases, the signal sampled through TEM can be perfectly recovered, in all practical applications, there are multiple non-idealities that lead to reconstruction errors both in the encoding and in the decoding processes. A long time window increases the condition number of the basis matrix, resulting in higher numerical error, which will be discussed next. The Gaussian basis is compact in the time domain; its basis matrix has a much lower condition number, resulting in smaller numerical error We found setting the window size to be four times the minimum signal period generally gives best results Another way to control the noise amplification problem is to use the pseudo-inverse of the coefficient matrix.
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