Optimum analog preprocessing for folding ADCs

Pace, P.E.; Schafer, J.L.; Styer, David

doi:10.1109/82.476181

Cited by 23 publications

(17 citation statements)

References 4 publications

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“…To effectively utilize symmetrical number systems, the dynamic range, M , defined as the greatest length of distinct, paired sequences (N −tuples) that contain no ambiguities, as well as its beginning position within the combined N −sequences must be known. Closedform expressions for M have been reported for the SNS and the OSNS in [1] and [2], respectively. Unlike the SNS and…”

Section: Introductionmentioning

confidence: 77%

Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

Pace

Stănică

Luke³

et al. 2014

IEEE Trans. Inform. Theory

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Abstract-The robust symmetrical number system (RSNS) is a number theoretic transform based on N ≥ 2 sequences that can extract the maximum amount of information from symmetrical folding waveforms. The sequences, based on coprime moduli, exhibit an integer Gray code property making the RSNS well-suited for many applications that benefit from an inherent error detection and correction capability such as analog-to-digital converters, direction finding arrays and radar waveform design. To use the RSNS, it is necessary to know the greatest length of combined sequences without ambiguities, called the dynamic range M , for which only a few closed-form expressions currently exist. In this paper, an efficient algorithm for computing M and its position within the combined set of sequences is presented and shown to be independent of the size of the moduli. The algorithm is used to generate the equations for several groups of additional moduli arrangements. Closed form expressions for M are conjectured and proved using the obtained congruence equations that define the ambiguity locations.

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Section: Introductionmentioning

confidence: 77%

Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

Pace

Stănică

Luke³

et al. 2014

IEEE Trans. Inform. Theory

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“…In 1989 Jayakumar et al proposed a O(n 2 ) near-maximal planarity testing algorithm [2] based on the PQ-tree technique [3]. Reference [4] presented a corrected and more generalized version of Jayakumar's algorithm. Reference [5] developed an O(m log n) algorithm for the maximal planar subgraph problem based on the Hopcroft-Tarjan planarity testing algorithm [6].…”

Section: An Efficient Parallel Algorithm For Planarization Problemmentioning

confidence: 99%

Two-channel RSNS dynamic range

Styer

Pace²

2002

IEEE Trans. Circuits Syst. I

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Symmetrical number systems have been explored for many applications in both analog and digital signal processing due to the common availability of symmetrical folding waveforms (e.g., cos ). The robust symmetrical number system (RSNS) is a modular scheme in which the integer values within each modulus, when considered together, change one at a time at the next code position (Gray code properties). Although the RSNS has a smaller dynamic range than the optimum symmetrical number system, the RSNS Gray code properties make it particularly attractive for error control. In the past, computer search algorithms have been used to determine the RSNS dynamic range (length of unambiguous vectors). In this brief, we define the two-channel RSNS and present a theorem that gives its dynamic range for relatively prime moduli , , 5. Index Terms-Dynamic range, Gray code properties, residue number system, robust symmetrical number system.

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“…Higher resolution in conversion is obtained when results from N different SNS moduli are recombined. Optimum Symmetrical Number System (OSNS) with a larger DR than that of SNS was proposed in [2]. Although the OSNS ADC uses fewer comparators, encoding errors occur when the input signal lies about any code transition point [2].…”

Section: Introductionmentioning

confidence: 99%

A novel approach for preprocessing analog signal using number theoretic transform

Pham

Premkumar

Madhukumar

2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

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In this paper, a preprocessing architecture for folding Analog-to-Digital converter (ADC) based on a new number system called Robust Folding Number System (RFNS) is presented. The RFNS is developed from robust symmetrical number system (RSNS) that was proposed by Pace et al [4]. The enhanced Dynamic Range (DR) of RFNS due to the introduction of the folding bit results in higher ADC resolution. The Symmetrical Residues (SRs) that are obtained in the intermediate step during processing of analog signals are converted to equivalent residues by simple mapping. This results in a conversion architecture that is less complex compared to that proposed in [6].

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Optimum analog preprocessing for folding ADCs

Cited by 23 publications

References 4 publications

Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

Two-channel RSNS dynamic range

A novel approach for preprocessing analog signal using number theoretic transform

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