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Several analog-to-digital conversion methods for bandlimited signals used in applications, such as Sigma Delta quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main tasks of modern signal processing, namely, at analog-to-digital (A/D) conversion in connection…
We study Sigma-Delta ($\Sigma\Delta$) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated…
A Delta-Sigma modulator that is often utilized to convert analog signals into digital signals can be modeled as a static uniform quantizer with an error feedback filter. In this paper, we present a rate-distortion analysis of quantizers…
In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…
Sampling above the Nyquist rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback…
Continuous-time Sigma-Delta (CT-$\Sigma\Delta$) modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are…
Sigma Delta quantization, a quantization method which first surfaced in the 1960s, has now been used widely in various digital products such as cameras, cell phones, radars, etc. The method samples an input signal at a rate higher than the…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…
In signal quantization, it is well-known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for…
In this paper we investigate encoding the bit-stream resulting from coarse Sigma-Delta quantization of finite frame expansions (i.e., overdetermined representations) of vectors. We show that for a wide range of finite-frames, including…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…
This paper considers the context of multiuser massive MIMO downlink precoding with low-resolution digital-to-analog converters (DACs) at the transmitter. This subject is motivated by the consideration that it is expensive to employ…
Suppose that the collection $\{e_i\}_{i=1}^m$ forms a frame for $\R^k$, where each entry of the vector $e_i$ is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We…