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

  title={Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise-affine maps},
  author={Rachel A. Ward},
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 onset of vanishing input. In the process, we prove that the origin is a globally attractive fixed point for the related family of asymmetrically damped piecewise-affine maps. Our proof of convergence is twofold: first, we construct a trapping set using a Lyapunov-type argument; we then take advantage of… 

Figures from this paper


Stability analysis for several second-order Sigma—Delta methods of coarse quantization of bandlimited functions
It is proved that there exists a bounded region that remains positively invariant under the two-dimensional piecewise-affine discrete dynamical system associated with each of these quantizers.
Novel schemes for sigma-delta modulation: from improved exponential accuracy to low-complexity design
This thesis constructs the first family of provably stable modulators of this type for all orders and introduces a novel, generalized stability criterion for Sigma-Delta modulation, which is crucial to achieve satisfactory approximation.
One‐bit sigma‐delta quantization with exponential accuracy
An infinite family of one‐bit sigma‐delta quantization schemes is constructed and it is proved that the error signal for π‐bandlimited signals is at most O(2−.07λ).
Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order
This paper focuses on a particular class of A/D conversion schemes adapted to audio signals, which need to be reconverted to an analog signal that can be understood by a human hearing system; the authors thus need a D/A conversion there.
A comparison of dithered and chaotic sigma-delta modulators
Two approaches are compared with regard to efficacy by simulating high-resolution sigma-delta modulators suitable for audio-conversion applications.
The benefits of multibit chaotic sigma delta modulation.
It is shown that minor variations on a traditional first order sigma-delta modulator, together with a multibit implementation, may be used to produce an effective, stable chaotic modulator that accurately encodes the input and helps remove the presence of idle tones.
On Robustness Properties of Beta Encoders and Golden Ratio Encoders
  • R. Ward
  • Computer Science
    IEEE Transactions on Information Theory
  • 2008
This paper presents a method whereby exponentially precise approximations to the value of beta in both GREs and beta encoders can be recovered amidst imprecise circuit components from the truncated beta expansions of a rdquotestrdquo number x testisin[-1, 1] and its negative counterpart -x test.
The effect of integrator leak in Sigma - Delta modulation
A method is presented which makes it possible to determine exactly the effect of integrator leak on the performance of the single-loop Sigma - Delta modulator with DC input. Theory from the field of