Sigma-delta modulation with i.i.d. Gaussian inputs

Author

Wong, Ping Wah ; Gray, Robert M.

Author_Institution

Dept. of Electr. & Comput. Eng., Clarkson Univ., Potsdam, NY, USA

Volume

36

Issue

4

fYear

1990

fDate

7/1/1990 12:00:00 AM

Firstpage

784

Lastpage

798

Abstract

The response of a single-loop sigma-delta modulator to an independent identically distributed (i.i.d.) Gaussian input signal is analyzed. A continuous-time stochastic model is developed and the connection of the model to the system is described. A condition is given so that the difference between the behavior of the model and that of the true system can be made arbitrarily small. Theories from renewal and Wiener processes are applied to show the convergence and mixing properties of the output sequence. Also derived is the power spectrum of the quantization noise. Compared to the spectrum when the input is DC, the i.i.d. Gaussian random process smears the discrete spectrum into band structures

Keywords

analogue-digital conversion; convergence; delta modulation; stochastic processes; A/D convertor; Gaussian inputs; Wiener processes; continuous-time stochastic model; convergence; independent identically distributed input signal; mixing properties; power spectrum; quantization noise; random process; renewal processes; sigma delta modulation; single-loop sigma-delta modulator; Decoding; Delta-sigma modulation; Frequency; Information systems; Laboratories; Quantization; Random processes; Signal processing; Signal resolution; Very large scale integration;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.53738

Filename

53738