Logic Operators on Delta-Sigma Bit-Streams

The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of Δ Σ -modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e., the logi...

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Bibliographic Details
Published in:Mathematical and computational applications Vol. 23; no. 1; p. 4
Main Author: Klein, Axel
Format: Journal Article
Language:English
Published: MDPI AG 01.03.2018
Subjects:
delta-sigma
logic
nonlinear operations
signal processing
ISSN:2297-8747, 2297-8747
Online Access:Get full text
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Summary:The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of Δ Σ -modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e., the logic function XOR results in the negative multiplication of two bipolar bit-streams, and the logic function AND results in the multiplication of two unipolar bit-streams. As the results are valid for bit-streams with independent high-frequency components, the normed cross-product is utilized for evaluation of the independence of the high-frequency components. In order to achieve a high independence between the input bit-streams, representing the same value, the quantization noise is affected. Multiple strategies are examined and Δ Σ -modulators with different designs are chosen as the best-suited solution. The operations are evaluated on a testbench.
ISSN:2297-8747
2297-8747
DOI:10.3390/mca23010004