Self-Reset ADC Modulo Sampling Without Fold Counting
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Solution Overview
Problem
Conventional ADCs face challenges in accurately reconstructing bandlimited signals due to saturation and clipping, especially when the dynamic range is large, and existing recovery methods for self-reset ADCs are inefficient and require knowledge of fold counts.
Innovation Solution
Implementing a self-reset ADC that performs centered modulo sampling at a rate greater than πe samples per second, allowing for accurate recovery of bandlimited signals without counting fold resets, by leveraging finite difference approximations and antidifference operations to reconstruct the signal as equal to the original plus a constant bias.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional ADCs are used to sample signals with large dynamic range, then the sampling process is simple, but the ADC saturates or clips causing distorted and erroneous reconstruction
Solution Approach 1:
The patent changes the functional parameter of the ADC by implementing a self-reset mechanism that performs modulo operations on the sampled signal. This transforms the ADC behavior from conventional linear sampling to modular sampling, allowing the output to wrap around when exceeding the full-scale range, thereby preventing saturation and clipping while preserving signal information for later recovery.
2Measurement precision
If self-reset ADCs are used to avoid clipping, then signal dynamic range handling is improved, but conventional recovery methods require knowledge of fold counts adding hardware complexity
Solution Approach 1:
The patent extracts and removes the fold counting function from the ADC hardware itself. Instead of requiring the ADC to count and store fold information, the invention uses mathematical recovery algorithms that operate solely on the modulo samples to reconstruct the original signal, thereby eliminating the need for additional hardware counters and memory storage for fold data.
Solution Approach 2:
The patent replaces the mechanical/hardware-based fold counting mechanism with a mathematical/software-based recovery algorithm. The reconstruction process uses computational mathematics (modulo arithmetic and signal processing algorithms) to infer the original signal from the folded samples without requiring physical counters or additional hardware components.
3Reliability
If oversampling at rate greater than πe is performed, then signal recovery is mathematically guaranteed, but the sampling rate is much higher than the Nyquist rate increasing data processing load
Solution Approach 1:
The patent applies partial oversampling by using a sampling rate that exceeds the Nyquist rate (specifically greater than πe) to provide mathematical guarantees for recovery, but not excessively higher than necessary. This balanced approach ensures reliable signal reconstruction while avoiding the inefficiency of extreme oversampling, processing only the minimal amount of additional data required for mathematical certainty.
Data Source
AI summary
A self-reset ADC may take a set of temporally equidistant, modulo samples of a bandlimited, analog signal, at a sampling rate that is greater than πe samples per second, where π is Archimedes' constant and is Euler's number. The bandlimited signal may have a bandwidth of 1 Hertz and a maximum frequency of 0.5 Hertz. These conditions of sampling rate, bandwidth and maximum frequency may ensure that an estimated signal may be recovered from the set of modulo samples. This estimated signal may be equal to the bandlimited signal plus a constant. The constant may be equal to an integer multiple of the modulus of the centered modulo operation employed to take the modulo samples.