Harmonic Analysis and Signal Processing Seminar
On unlimited sampling and reconstruction
Tuesday, October 1, 2019, 2pm, WWH 1314
Shannon’s sampling theorem provides a link between the continuous and the discrete realms stating that a bandlimited signal is uniquely determined by its values on a discrete set. This cornerstone topic is well understood and explored, both mathematically and algorithmically. However, its practical realization via analog-to-digital converters (ADCs) still suffers from a severe bottleneck due to the fundamental assumption that the samples can span an arbitrary range of amplitudes. Unlike Shannon’s sampling theorem, ADCs are limited in dynamic range and saturate whenever the signal amplitude exceeds the maximum recordable ADC voltage thus leading to a significant information loss. The recent theory of Unlimited Sampling circumvents this dynamic range problem and yields that a bandlimited function with high dynamic range can be recovered exactly from oversampled, low dynamic range samples obtained via modulo operation. In this talk, we will discuss key aspects of this new setup: sufficient conditions that guarantee perfect recovery from modulo samples, stable recovery algorithm, implementation via so called self-reset ADCs. We will also make a further step in practical direction by coupling modulo sampling with one-bit quantization. We will provide a constructive recovery algorithm for bandlimited signals from one-bit modulo samples and complement it with a bound on the reconstruction error.