# On Robustness Properties of Beta Encoders and Golden Ratio Encoders

@article{Ward2008OnRP, title={On Robustness Properties of Beta Encoders and Golden Ratio Encoders}, author={R. Ward}, journal={IEEE Transactions on Information Theory}, year={2008}, volume={54}, pages={4324-4334} }

The beta encoder was recently proposed as a quantization scheme for analog-to-digital (A/D) conversion; in contrast to classical binary quantization, in which each analog sample xisin[-1, 1] is mapped to the first N bits of its base-2 expansion, beta encoders replace each sample x with its expansion in a base beta between 1<beta<2. This expansion is nonunique when 1<beta<2, and the beta encoder exploits this redundancy to correct inevitable errors made by the quantizer component of its circuit… Expand

#### 13 Citations

Beta encoders: Symbolic Dynamics and Electronic Implementation

- Mathematics, Computer Science
- Int. J. Bifurc. Chaos
- 2012

A new class of analog-to-digital (A/D) and digital- to-analog (D/A) converters that uses a flaky quantizer that has been shown to have exponential bit rate accuracy and a self-correcting property for fluctuations of the amplifier factor β and quantizer threshold ν and it is demonstrated that chaotic attractors can be observed experimentally from these β-encoder circuits. Expand

β-expansion attractors observed in A/D converters.

- Mathematics, Medicine
- Chaos
- 2012

The object of this paper is to observe the embedded attractors in the β-encoder and to identify attractors that are useful for spread-spectrum codes and optimization techniques using pseudo-random numbers. Expand

Mathematics of Analog‐to‐Digital Conversion

- Mathematics
- 2012

As the performance of digital circuits and the capacity of digital communication channels have advanced steadily over the past decades, digital signals have replaced analog signals in nearly every… Expand

Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise-affine maps

- Mathematics
- 2010

In this paper, we introduce a family of second-order sigma delta quantization schemes for analog-to-digital conversion which are 'quiet': quantization output is guaranteed to fall to zero at the… Expand

Fibonacci sequence, golden section, Kalman filter and optimal control

- Mathematics, Computer Science
- Signal Process.
- 2009

It is shown that, for a scalar random walk system in which the two noise sources have equal variance, the Kalman filter's estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the Fibonacci numbers. Expand

Generalized phi number system and its applications for image decomposition and enhancement

- Computer Science, Engineering
- Electronic Imaging
- 2011

This paper introduces a new class of parameterized number systems, namely the generalized Phi number system (GPNS), which derives the traditional PhiNumber system, binary number system, beta encoder, and other commonly used number systems by selecting appropriate parameters. Expand

Random walks associated to beta-shifts.

- Mathematics
- 2019

We study the dynamics of a simple random walk on subshifts defined by the beta transformation and apply it to find concrete formulae for the Hausdorff dimension of digit frequency sets for $\beta>1$… Expand

Second-order hyperbolic Fuchsian systems and applications

- Physics, Mathematics
- 2010

We introduce a new class of singular partial differential equations, referred to as the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are… Expand

O ct 2 01 9 RANDOM WALKS ASSOCIATED TO BETA-SHIFTS

- 2019

We study the dynamics of a simple random walk on subshifts defined by the beta transformation and apply it to find concrete formulae for the Hausdorff dimension of digit frequency sets for β > 1 that… Expand

Some Infinite Sums Related to the \(k\)-Fibonacci Numbers

- Mathematics
- 2018

In this study, some infinite sums related to the \(k\)-Fibonacci numbers have been obtained by using in
nite sums related to classic Fibonacci numbers in literature.

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