Signal Processing in Spike Domain

Since the 1980s, when digital signal processing took off, signals have typically been sampled and processed uniformly in time. This practice is largely guided by the Nyquist Shannon-Kotelnikov theorem, which guarantees accurate signal reconstruction as long as the sampling rate exceeds twice the signal’s maximum frequency component. This worst-case approach has a significant drawback. It leads to oversampling during periods where the high frequency components are not present in the input signal.
An event-based sampling approach that adapts to local signal properties can remedy this. Threshold-based sampling (TBS), also known as level-crossing sampling (LC), was introduced as such a sampling paradigm. Data is only sampled when the amplitude of the input changes by a certain threshold. The resulting sampling sequence, a so-called spike train, encodes the samples with their positions in time and the directions of the relative amplitude changes.
While several LC-ADC architectures have been published, there is a lack of signal processing algorithms designed for the non-uniform time-quantized sampling sequences. The core of this thesis is the development of algorithms that exploit the sparsity of the input samples. To pave the way to fully event-based signal processing chains, tailored finite impulse response (FIR) evaluation techniques are proposed to remove noise-induced or distortion-induced samples and reduce activity in subsequent stages. Existing algorithms store oversampled impulse responses requiring immense look-up tables (LUTs). The concepts in this work can reduce the required FIR coefficient storage down to 3% with a computational complexity that scales with the input spike density rather than their fine time resolution.
On the example of a speech command processing task, it is demonstrated how the combination of event-based sampling and a proposed filter concept (IC-CIR w\MA) yields a signal-to-noise ratio (SNR) improvement of 6.73dB while compressing the samples to 8.52%. This was achieved requiring 34% of the multiplications and 97% of the additions compared to the conventional FIR evaluation at a fixed rate of 24kHz. The Free Lossless Audio Codec (FLAC) encoded file storing the speech commands is reduced in size from 184kB to 17.4kB (9%).