Playing with time: Dilation and time encoding

doi:10.1016/j.acha.2026.101921

Playing with time: Dilation and time encoding

2026-09-01

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DOI：10.1016/j.acha.2026.101921

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The samples resulting from a time encoding machine (TEM) are intrinsically non-uniform and thus typical strategies for reconstruction rely on transforming the time encoded samples into an equivalent non-uniform sampling problem. In this work we take an alternative perspective and consider how integrate-and-fire time encoded samples represent uniform sampling on an equivalent 'amplitude'-domain signal. From this perspective, existing reconstruction strategies are readily applicable but only for a limited class of signals. To remedy this, we propose a modification of the typical sampling hardware to create a new time-dilating integrate-and-fire sampler (TDIF) that can sample and reconstruct a broader range of signals. We show that, in amplitude-domain, dilation of time measurements is an almost equivalent operation to filtering in the time-domain. Thus signals can be sampled with arbitrary sampling kernels in amplitude-domain by dilating time measurements. We show that non-negative piecewise constant signals can be perfectly reconstructed from their sparse dilated time encodings.

Keywords:

Time encoding

Sampling

Finite rate of innovation

Playing with time: Dilation and time encoding

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