Methods and Apparatus for Modulo Sampling and Recovery
AssigneeMassachusetts Institute of Technology
InventorsAyush Bhandari, Felix Krahmer, Ramesh Raskar
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Abstract
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.
Claims20
A method comprising sampling a first analog signal at uniformly spaced times at a sampling rate that is greater than Ire samples per second, wherein
- (a) e is Euler's number;
- (b) π is Archimedes' constant;
- (c) the first signal has a bandwidth of 1 Hertz and a maximum frequency of 0.5 Hertz;
- (d) the sampling includes performing a centered modulo operation, which centered modulo operation has a modulus;
- and
- (e) the method includes performing a calculation that
- (i) takes, as an input, a set of modulo samples created by the sampling,
- (ii) includes computing finite difference approximations of higher order derivatives of the set of modulo samples, and
- (iii) outputs an estimate of the first signal, which estimate is equal to the first signal plus a constant, which constant is an integer multiple of the modulus.
A method comprising sampling a first analog signal at uniformly spaced times at a sampling rate that is greater than Ire samples per second, wherein
- (a) e is Euler's number;
- (b) π is Archimedes' constant;
- (c) the first signal has a bandwidth of 1 Hertz and a maximum frequency of 0.5 Hertz;
- and
- (d) the sampling includes performing a centered modulo operation.
An apparatus that comprises an analog-to-digital converter (ADC), which ADC is configured to sample a first analog signal at uniformly spaced times at a sampling rate that is greater than Ire samples per second, in such a way that the sampling includes performing a centered modulo operation, wherein:
- (a) e is Euler's number;
- (b) π is Archimedes' constant;
- and
- (c) the first signal has a bandwidth of 1 Hertz and a maximum frequency of 0.5 Hertz.
Dependencies are inferred from the claim text.