Number theoretical error estimates in a quantization scheme for bandlimited signals
C. Si̇nan Güntürk · DIMACS series in discrete mathematics and theoretical computer science · 2004
Sigma-delta quantization is a way of representing bandlimited signals (functions with compactly supported Fourier transforms) by {0, 1} sequences for each sampling density such that convolving these sequences with appropriately chosen filters produces approximations of the original signals. Approximations are refined by increasing the sampling density; this is what makes such a scheme fundamentally different from more conventional quantization schemes, where the sampling density is not varied. We present various examples of how tools from analytic number theory are employed in sharpening the error estimates in sigma-delta systems.