# Over the Limits of Traditional Sampling: Advantages and Issues of AICs for Measurement Instrumentation

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## Abstract

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## 1. Introduction

## 2. Wideband Acquisition from Nyquist-Shannon to CS Paradigm

## 3. Analog-to-Information Converters

#### Acquisition and Reconstruction

## 4. Metrological Characterization in AICs

#### 4.1. Characterization Procedure for AICs

#### 4.2. Experimental Testing of AICs

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Kirolos, S.; Laska, J.; Wakin, M.; Duarte, M.; Baron, D.; Ragheb, T.; Massoud, Y.; Baraniuk, R. Analog-to-Information Conversion via Random Demodulation. In Proceedings of the IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software, Richardson, TX, USA, 29–30 October 2006; pp. 71–74. [Google Scholar]
- Laska, J.N.; Kirolos, S.; Duarte, M.F.; Ragheb, T.S.; Baraniuk, R.G.; Massoud, Y. Theory and Implementation of an Analog-to-Information Converter using Random Demodulation. In Proceedings of the IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, 27–30 May 2007; pp. 1959–1962. [Google Scholar]
- Iadarola, G. Characterization of Analog-to-Information Converters [imsawards]. IEEE Instrum. Meas. Mag.
**2022**, 25, 98–99. [Google Scholar] [CrossRef] - Zhao, Y.; Wang, H.; Zheng, Y.; Zhuang, Y.; Zhou, N. High sampling rate or high resolution in a sub-Nyquist sampling system. Measurement
**2020**, 166, 108175. [Google Scholar] [CrossRef] - Candès, E.J.; Romberg, J.; Tao, T. Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information. IEEE Trans. Inf. Theory
**2006**, 52, 489–509. [Google Scholar] [CrossRef] [Green Version] - Chen, X.; Yu, Z.; Hoyos, S.; Sadler, B.M.; Silva-Martinez, J. A Sub-Nyquist Rate Sampling Receiver Exploiting Compressive Sensing. IEEE Trans. Circuits Syst. I Regul. Pap.
**2011**, 58, 507–520. [Google Scholar] [CrossRef] - Haque, T.; Yazicigil, R.T.; Pan, K.J.; Wright, J.; Kinget, P.R. Theory and Design of a Quadrature Analog-to-Information Converter for Energy-Efficient Wideband Spectrum Sensing. IEEE Trans. Circuits Syst. I Regul. Pap.
**2015**, 62, 527–535. [Google Scholar] [CrossRef] - Nam, H.; Park, J.; Park, J.D. A 2–18 GHz Compressed Sensing Receiver With Broadband LO Chain in 0.13-μm BiCMOS. IEEE Microw. Wirel. Compon. Lett.
**2019**, 29, 620–622. [Google Scholar] [CrossRef] - Pelissier, M.; Masson, G.; Ouvry, L.; Dias, L.F.F.; Marnat, M. Hardware platform of Analog-to-Information converter using Non Uniform Wavelet Bandpass Sampling for RF signal activity detection. In Proceedings of the IEEE International Symposium on Circuits and Systems, Florence, Italy, 27–30 May 2018. [Google Scholar]
- Abari, O.; Lim, F.; Chen, F.; Stojanović, V. Why Analog-to-Information Converters Suffer in High-Bandwidth Sparse Signal Applications. IEEE Trans. Circuits Syst. I Regul. Pap.
**2013**, 60, 2273–2284. [Google Scholar] [CrossRef] - Pang, Z.; Yuan, M.; Wakin, M.B. A random demodulation architecture for sub-sampling acoustic emission signals in structural health monitoring. J. Sound Vib.
**2018**, 431, 390–404. [Google Scholar] [CrossRef] - Iadarola, G.; Spinsante, S.; De Vito, L.; Lamonaca, F. A support for signal compression in living environments: The Analog-to-Information Converter. In Proceedings of the 2022 IEEE International Workshop on Metrology for Living Environment (MetroLivEn), Cosenza, Italy, 25–27 May 2022; pp. 292–297. [Google Scholar]
- Ravelomanantsoa, A.; Rabah, H.; Rouane, A. Simple and Efficient Compressed Sensing Encoder for Wireless Body Area Network. IEEE Trans. Instrum. Meas.
**2014**, 63, 2973–2982. [Google Scholar] [CrossRef] - Gangopadhyay, D.; Allstot, E.G.; Dixon, A.M.R.; Natarajan, K.; Gupta, S.; Allstot, D.J. Compressed Sensing Analog Front-End for Bio-Sensor Applications. IEEE J. Solid-State Circuits
**2014**, 49, 426–438. [Google Scholar] [CrossRef] - Lu, F.; Cao, Z.; Xie, Y.; Xu, L. Precise wide-band electrical impedance spectroscopy measurement via an ADC operated below the Nyquist sampling rate. Measurement
**2021**, 174, 108995. [Google Scholar] [CrossRef] - Daponte, P.; De Vito, L.; Iadarola, G.; Spinsante, S. PRBS Selection for Velocity Measurements with Compressive Sampling-Based DS-CDMA Radio Navigation Receivers. In Proceedings of the IEEE International Workshop on Metrology for Aerospace, Rome, Italy, 20–22 June 2018; pp. 305–310. [Google Scholar]
- Maleh, R.; Fudge, G.L.; Boyle, F.A.; Pace, P.E. Analog-to-Information and the Nyquist Folding Receiver. IEEE J. Emerg. Sel. Top. Circuits Syst.
**2012**, 2, 564–578. [Google Scholar] [CrossRef] - Liu, W.; Huang, Z.; Wang, X.; Sun, W. Design of a Single Channel Modulated Wideband Converter for Wideband Spectrum Sensing: Theory, Architecture and Hardware Implementation. Sensors
**2017**, 17, 1035. [Google Scholar] [CrossRef] [Green Version] - Zhao, Y.; Hu, Y.H.; Liu, J. Random Triggering-Based Sub-Nyquist Sampling System for Sparse Multiband Signal. IEEE Trans. Instrum. Meas.
**2017**, 66, 1789–1797. [Google Scholar] [CrossRef] [Green Version] - De Vito, L.; Iadarola, G.; Lamonaca, F.; Picariello, F.; Rapuano, S.; Tudosa, I. Non-Uniform Wavelet Bandpass Sampling Analog-to-Information Converter: A hardware implementation and its experimental assessment. Measurement
**2019**, 134, 739–749. [Google Scholar] [CrossRef] - Mishali, M.; Eldar, Y.C.; Dounaevsky, O.; Shoshan, E. Xampling: Analog to digital at sub-Nyquist rates. IET Circuits Devices Syst.
**2011**, 5, 8–20. [Google Scholar] [CrossRef] - Baransky, E.; Itzhak, G.; Wagner, N.; Shmuel, I.; Shoshan, E.; Eldar, Y. Sub-Nyquist radar prototype: Hardware and algorithm. IEEE Trans. Aerosp. Electron. Syst.
**2014**, 50, 809–822. [Google Scholar] [CrossRef] - Yoo, J.; Turnes, C.; Nakamura, E.B.; Le, C.K.; Becker, S.; Sovero, E.A.; Wakin, M.B.; Grant, M.C.; Romberg, J.; Emami-Neyestanak, A.; et al. A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition. IEEE J. Emerg. Sel. Top. Circuits Syst.
**2012**, 2, 626–638. [Google Scholar] [CrossRef] [Green Version] - Yoo, J.; Becker, S.; Loh, M.; Monge, M.; Candes, E.; Emami-Neyestanak, A. A 100 MHz–2 GHz 12.5× sub-Nyquist rate receiver in 90 nm CMOS. In Proceedings of the 2012 IEEE Radio Frequency Integrated Circuits Symposium, Montreal, QC, Canada, 17–19 June 2012; pp. 31–34. [Google Scholar]
- Wakin, M.; Becker, S.; Nakamura, E.; Grant, M.; Sovero, E.; Ching, D.; Yoo, J.; Romberg, J.; Emami-Neyestanak, A.; Candes, E. A Nonuniform Sampler for Wideband Spectrally-Sparse Environments. IEEE J. Emerg. Sel. Top. Circuits Syst.
**2012**, 2, 516–529. [Google Scholar] [CrossRef] [Green Version] - Donoho, D.L.; Huo, X. Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory
**2001**, 47, 2845–2862. [Google Scholar] [CrossRef] - Candes, E.; Romberg, J. Sparsity and Incoherence in Compressive Sampling. Inverse Probl.
**2007**, 23, 696–985. [Google Scholar] [CrossRef] [Green Version] - Daponte, P.; De Vito, L.; Iadarola, G.; Rapuano, S. A reduced-code method for integral nonlinearity testing in DACs. Measurement
**2021**, 182, 109764. [Google Scholar] [CrossRef] - Šaliga, J.; Andráš, I.; Dolinský, P.; Michaeli, L.; Kováč, O.; Kromka, J. ECG compressed sensing method with high compression ratio and dynamic model reconstruction. Measurement
**2021**, 183, 109803. [Google Scholar] [CrossRef] - Daponte, P.; De Vito, L.; Iadarola, G.; Picariello, F.; Rapuano, S. Deterministic Compressed Sensing of heart sound signals. In Proceedings of the 2021 IEEE International Symposium on Medical Measurements and Applications (MeMeA), Lausanne, Switzerland, 23–25 June 2021; pp. 1–6. [Google Scholar]
- Daponte, P.; De Vito, L.; Iadarola, G.; Picariello, F. ECG Monitoring Based on Dynamic Compressed Sensing of Multi-Lead Signals. Sensors
**2021**, 21, 7003. [Google Scholar] [CrossRef] [PubMed] - Iadarola, G.; Poli, A.; Spinsante, S. Compressed Sensing of Skin Conductance Level for IoT-based wearable sensors. In Proceedings of the 2022 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Ottawa, ON, Canada, 16–19 May 2022; pp. 1–6. [Google Scholar]
- Mishali, M.; Eldar, Y. From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals. IEEE J. Sel. Top. Signal Process.
**2010**, 4, 375–391. [Google Scholar] [CrossRef] [Green Version] - IEEE Std 1241-2010; IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters. IEEE: Piscataway, NJ, USA, 2011.
- Donoho, D.; Elad, M.; Temlyakov, V. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory
**2006**, 52, 6–18. [Google Scholar] [CrossRef] - Herman, M.A.; Needell, D. Mixed operators in compressed sensing. In Proceedings of the 44th Annual Conference on Information Sciences and Systems, Princeton, NJ, USA, 17–19 March 2010; pp. 1–6. [Google Scholar]
- Herman, M.A.; Strohmer, T. General Deviants: An Analysis of Perturbations in Compressed Sensing. IEEE J. Sel. Top. Signal Process.
**2010**, 4, 342–349. [Google Scholar] [CrossRef] [Green Version] - De Vito, L.; Jendzurski, J.; Rapuano, S.; Boyer, W.B.; Blair, J.; Paulter, N.G. The IEEE Technical Committee 10-The Waveform Generation, Measurement, and Analysis Committee: Update 2021. IEEE Instrum. Meas. Mag.
**2022**, 25, 16–18. [Google Scholar] [CrossRef] - Ragheb, T.; Laska, J.N.; Nejati, H.; Kirolos, S.; Baraniuk, R.G.; Massoud, Y. A prototype hardware for random demodulation based compressive analog-to-digital conversion. In Proceedings of the 51st Midwest Symposium on Circuits and Systems, Knoxville, TN, USA, 10–13 August 2008; pp. 37–40. [Google Scholar]
- Laska, J.N.; Slavinsky, J.P.; Baraniuk, R.G. The polyphase random demodulator for wideband compressive sensing. In Proceedings of the Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), Pacific Grove, CA, USA, 6–9 November 2011; pp. 515–519. [Google Scholar]
- Nader, C.; Van Moer, W.; Bjorsell, N.; Barbe, K.; Handel, P. Reducing the Analog and Digital Bandwidth Requirements of RF Receivers for Measuring Periodic Sparse Waveforms. IEEE Trans. Instrum. Meas.
**2012**, 61, 2960–2971. [Google Scholar] [CrossRef] - Zhuang, X.; Yuan, X. Calibration of Analog to Information Converter based Sampling System. In Proceedings of the 2021 IEEE 15th International Conference on Electronic Measurement & Instruments (ICEMI), Nanjing, China, 29–31 October 2021; pp. 224–227. [Google Scholar]
- Daponte, P.; De Vito, L.; Iadarola, G.; Rapuano, S. PRBS non-idealities affecting Random Demodulation Analog-to-Information Converters. In Proceedings of the 21st IMEKO TC-4 International Symposium on Understanding the World through Electrical and Electronic Measurement and 19th IMEKO International Workshop on ADC Modelling and Testing, Budapest, Hungary, 7–9 September 2016; pp. 71–76. [Google Scholar]
- Daponte, P.; De Vito, L.; Iadarola, G.; Iovini, M.; Rapuano, S. Experimental comparison of two mathematical models for Analog-to-Information Converters. In Proceedings of the 21st IMEKO TC-4 International Symposium on Understanding the World through Electrical and Electronic Measurement and 19th IMEKO International Workshop on ADC Modelling and Testing, Budapest, Hungary, 7–9 September 2016; pp. 65–70. [Google Scholar]
- Daponte, P.; De Vito, L.; Iadarola, G.; Rapuano, S. Analog Multiplication in Random Demodulation Analog-to-Information Converters. J. Phys. Conf. Ser.
**2018**, 1065. [Google Scholar] [CrossRef] - Pankiewicz, P.J.; Arildsen, T.; Larsen, T. Sensitivity of the random demodulation framework to filter tolerances. In Proceedings of the 19th European Signal Processing Converence, Barcelona, Spain, 29 August–2 September 2011; pp. 534–538. [Google Scholar]
- Daponte, P.; De Vito, L.; Iadarola, G.; Rapuano, S. Experimental Characterization of a RF Mixer for Wideband Data Acquisition Systems. In Proceedings of the IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Turin, Italy, 22–25 May 2017; pp. 1–6. [Google Scholar]
- IEEE Std 2414-2020; IEEE Standard for Jitter and Phase Noise. IEEE: Piscataway, NJ, USA, 2021.

**Figure 1.**Comparison between the data acquisition systems implementing compression: (

**a**) sample-then-compress paradigm and (

**b**) CS paradigm.

**Figure 2.**Generic framework of an AIC with its two sections: the acquisition front-end and the reconstruction back-end.

**Figure 3.**Experimental results of ME in the RD for (

**a**) the time domain model and (

**b**) the frequency domain model [44].

**Figure 4.**Numerical results of ME in the RD versus (

**a**) Duty Cycle Distortion and (

**b**) Random Jitter [43].

**Figure 5.**Experimental results of ME in the RD based on (

**a**) the mixer and (

**b**) the analog multiplier [45].

Advantages | Limitations |
---|---|

Lower sampling frequency | Sparsity requirement on input signal |

Lower data rate | More computational load for back-end |

Reduced occupancy of acquisition memory | Architectural complexity [7,8,9] |

Reduced power consumption [6,7] | Difficult uncertainty evaluation |

High compression in recent architectures [8,9] | More sensitivity to non-idealities [10] |

Broadband input in recent architectures [8,9] | Intricate front-end characterization [3,6] |

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**MDPI and ACS Style**

Iadarola, G.; Daponte, P.; De Vito, L.; Rapuano, S.
Over the Limits of Traditional Sampling: Advantages and Issues of AICs for Measurement Instrumentation. *Sensors* **2023**, *23*, 861.
https://doi.org/10.3390/s23020861

**AMA Style**

Iadarola G, Daponte P, De Vito L, Rapuano S.
Over the Limits of Traditional Sampling: Advantages and Issues of AICs for Measurement Instrumentation. *Sensors*. 2023; 23(2):861.
https://doi.org/10.3390/s23020861

**Chicago/Turabian Style**

Iadarola, Grazia, Pasquale Daponte, Luca De Vito, and Sergio Rapuano.
2023. "Over the Limits of Traditional Sampling: Advantages and Issues of AICs for Measurement Instrumentation" *Sensors* 23, no. 2: 861.
https://doi.org/10.3390/s23020861