TY - GEN
T1 - Unlimited Sampling of Sparse Sinusoidal Mixtures
AU - Bhandari, Ayush
AU - Krahmer, Felix
AU - Raskar, Ramesh
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/15
Y1 - 2018/8/15
N2 - In parallel to Shannon's sampling theorem, the recent theory of unlimited sampling yields that a bandlimited function with high dynamic range can be recovered exactly from oversampled, low dynamic range samples. In this way, the unlimited sampling methodology circumvents the dynamic range problem that limits the use of conventional analog-to-digital converters (ADCs) which are prone to clipping or saturation problem. The unlimited sampling theorem is made practicable by using a unique ADC architecture-the self-reset ADC or the SR-ADC-which resets voltage before clipping, thus producing modulo or wrapped samples. While retaining full dynamic range of the input signal, surprisingly, the sampling density prescribed by the unlimited sampling theorem is independent of the maximum recordable voltage of the new ADC and depends only on the signal bandwidth. As the corresponding problem of signal recovery from such modulo samples arises in various applications with different signal models, where the original result does not directly apply, the original paper continues to trigger research follow-ups. In this paper, we investigate the case of sampling and reconstruction of a mixture of K sinusoids from such modulo samples. This problem is at the heart of spectral estimation theory and application areas include active sensing, ranging, source localization, interferometry and direction-of-arrival estimation. By relying on the SR-ADCs, we develop a method for recovery of K-sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation. As our signal model is completely characterized by K pairs of amplitudes and frequencies, we obtain a parametric sampling theorem; we complement it with a recovery algorithm. Numerical demonstrations validate the effectivity of our approach.
AB - In parallel to Shannon's sampling theorem, the recent theory of unlimited sampling yields that a bandlimited function with high dynamic range can be recovered exactly from oversampled, low dynamic range samples. In this way, the unlimited sampling methodology circumvents the dynamic range problem that limits the use of conventional analog-to-digital converters (ADCs) which are prone to clipping or saturation problem. The unlimited sampling theorem is made practicable by using a unique ADC architecture-the self-reset ADC or the SR-ADC-which resets voltage before clipping, thus producing modulo or wrapped samples. While retaining full dynamic range of the input signal, surprisingly, the sampling density prescribed by the unlimited sampling theorem is independent of the maximum recordable voltage of the new ADC and depends only on the signal bandwidth. As the corresponding problem of signal recovery from such modulo samples arises in various applications with different signal models, where the original result does not directly apply, the original paper continues to trigger research follow-ups. In this paper, we investigate the case of sampling and reconstruction of a mixture of K sinusoids from such modulo samples. This problem is at the heart of spectral estimation theory and application areas include active sensing, ranging, source localization, interferometry and direction-of-arrival estimation. By relying on the SR-ADCs, we develop a method for recovery of K-sparse, sum-of-sinusoids from finitely many wrapped samples, thus avoiding clipping or saturation. As our signal model is completely characterized by K pairs of amplitudes and frequencies, we obtain a parametric sampling theorem; we complement it with a recovery algorithm. Numerical demonstrations validate the effectivity of our approach.
UR - http://www.scopus.com/inward/record.url?scp=85052482559&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2018.8437122
DO - 10.1109/ISIT.2018.8437122
M3 - Conference contribution
AN - SCOPUS:85052482559
SN - 9781538647806
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 336
EP - 340
BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018
Y2 - 17 June 2018 through 22 June 2018
ER -