Algorithms for analog-to-digital conversion.


Alexander Powell

14:00:00 - 15:30:00

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

We shall discuss various algorithms related to the quantization of oversampled signal representations. Sampling aims to represent a signal in terms of a discrete collection of linear measurements. Quantization (analog-to-digital conversion) is the process discretizing the amplitudes of samples to render them amenable to digital storage and processing. We shall prove mean squared error bounds for consistent reconstruction (and iterative variants) when used to reconstruct a signal from frame coefficients that have been quantized under the uniform noise model for memoryless scalar quantization. For suitable sampling, these error bounds show that consistent reconstruction achieves essentially optimal mean squared error of order d^3/N^2 where N is the number of samples and d is the ambient dimension. We shall also discuss a more sophisticated class of quantizers, known as sigma-delta algorithms, which offers reduced quantization errors and desirable robustness properties; if time permits we shall describe error bounds for sigma-delta quantization in the settings of both redundant frames and compressive sampling.