2023/06/27 by Joy, Rohan, Felix Krahmer, Krahmer, Felix +4
Computer Science · Engineering · Mathematics · #41A29 #42C15 #94A12 #94A20 #Algorithm #Artificial intelligence #Bandlimiting #Computer science #Discrete mathematics #FOS: Computer and information sciences #Fourier transform #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Noise (video) #Physics #Quantization (signal processing) #Quantum mechanics #Random noise #Sigma #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2306.15758
openalex publication_date 2023/06/27 · openalex created_date 2023/06/30 · openalex updated_date 2026/07/28
Noise-shaping quantization techniques are widely used for converting bandlimited signals from the analog to the digital domain. They work by ``shaping" the quantization noise so that it falls close to the reconstruction operator's null space. We investigate the compatibility of two such schemes, specifically ΣΔ quantization and distributed noise-shaping quantization, with random samples of bandlimited functions. Suppose R>1 is a real number and assume that \xi\i=1m is a sequence of i.i.d random variables uniformly distributed on [-R,R], where R>R is appropriately chosen. We show that by using a noise-shaping quantizer to quantize the (randomly sign flipped) values of a real-valued π-bandlimited function f at \xi\i=1m, a function f\sharp can be reconstructed from these quantized values such that ‖f-f\sharp‖L2[-R, R] decays with high probability as m and R increase. This decay holds uniformly over all bandlimited f. We emphasize that the sample points \xi\i=1m are completely random, that is, they have no predefined structure, which makes our findings the first of their kind.