Optimum quantization of a class of non-bandlimited signals

We consider the quantization of a special class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. Similar to sigma-delta modulation ideas, we show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of these signals. We then consider noise shaping by optimizing a pre- and post filter around the quantizer and develop a closed form expression for the coding gain of the scheme under study. The use of an orthonormal filter bank as a sophisticated quantizer is investigated and several examples are provided

Components for oversampled signal processors

Oversampled converters trade transmission bandwidth for resolution. An idealized model gives an insight into the way in which signals are encoded and thus how they can be manipulated. Oversampling offers a form of signal processing that requires simple processing elements capable of exploiting the growing clock speeds available in integrated solutions. Simultaneously avoids the need for analog circuitry. This paper reviews common operations that can be performed on oversampled signals

Noise analysis of modulated quantizer based on oversampled signals

In this paper, a noise analysis of a modulated quantizer is performed. If input signals are oversampled, then the quantization error could be reduced by modulating both the input and the output of the quantizer. The working principle is based on the fact that convolutions of bandpass signals would spread wider in the frequency spectrum than that of lowpass signals. Hence, by filtering the high frequency components, the signal-to-noise ratio (SNR) could be increased. Numerical simulation results show that the modulated quantization scheme could achieve an average of 13.0960dB to 21.4700dB improvements on SNR over the conventional scheme, depends on the types of bandlimited input signals

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201