Sigma Delta Quantized Networks

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing

Suppose that the collection {ei}i=1 forms a frame for R, where each entry of the vector ei is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We show that an arbitrary signal in R can be recovered from its quantized frame coefficients up to an error which decays root-exponentially in the oversampling rate m/k. Here the...

Approximating a Bandlimited Function Using Very Coarsely Quantized Data: Improved Error Estimates in Sigma-delta Modulation

This paper concerns fine analytical error estimates in analog-to-digital conversion of bandlimited functions using the method of sigma-delta modulation (also called Σ∆ quantization). This method has found widespread usage in practice due to several advantages in its implementation compared to conventional methods (see [1, 11]). A recent mathematical treatment of this problem appears in [3]. Bel...

Generalized sigma-derivation on Banach algebras

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

Time-Mode Signal Quantization for Use in Sigma-Delta Modulators

The rapid scaling in modern CMOS technology has motivated the researchers to design new analog-to-digital converter (ADC) architectures that can properly work in lower supply voltage. An exchanging the data quantization procedure from the amplitude to the time domain, can be a promising alternative well adapt with the technology scaling. This paper is going to review the recent development in t...