Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system’s performance that supports the empirical observations.

Abstract—In applications where signal frequencies are high, but information bandwidths are low, analog-to-information converters (AICs) have been proposed as a potential solution to overcome the resolution and performance limitations of high-speed analog-to-digital converters (ADCs). However, the hardware implementation of such systems has yet to be evaluated. This paper aims to fill this gap, by evaluating the impact of circuit impairments on per-formance limitations and energy cost of AICs. We point out that although the AIC architecture facilitates slower ADCs, the signal encoding, typically realized with a mixer-like circuit, still occurs at the Nyquist frequency of the input to avoid aliasing. We illustrate that the jitter and aperture of this mixing stage limit the achiev-able AIC resolution. In order to do so, we designed an end-to-end system evaluation framework for examining these limitations, as well as the relative energy-efficiency of AICs versus high-speed ADCs across the resolution, receiver gain and signal sparsity. The evaluation shows that the currently proposed AICs have no per-formance benefits over high-speed ADCs. However, AICs enable 2–10X in energy savings in low to moderate resolution (ENOB), low gain applications. Index Terms—Analog-to-digital converter (ADC), analog-to-in-formation converter (AIC), compressed sensing (CS).

The notion of regularization has been widely used as a tool to address a number of problems that are usually encountered in Machine Learning. Improving the performance of an estimator by shrinking the norm of the MVU estimator, guarding against overfitting, coping with ill-conditioning, provid-

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Abstract—In applications where signal frequencies are high, but information bandwidths are low, analog-to-information converters (AICs) have been proposed as a potential solution to overcome the resolution and performance limitations of high-speed analog-todigital converters (ADCs). However, the hardware implementation of such systems has yet to be evaluated. This paper aims to fill this gap, by evaluating the impact of circuit impairments on performance limitations and energy cost of AICs. We point out that although the AIC architecture facilitates slower ADCs, the signal encoding, typically realized with a mixer-like circuit, still occurs at the Nyquist frequency of the input to avoid aliasing. We illustrate that the jitter and aperture of this mixing stage limit the achievable AIC resolution. In order to do so, we designed an end-to-end system evaluation framework for examining these limitations, as well as the relative energy-efficiency of AICs versus high-speed ADCs across the resolution, receiver gain and signal sparsity. The evaluation shows that the currently proposed AICs have no performance benefits over high-speed ADCs. However, AICs enable 2–10X in energy savings in low to moderate resolution (ENOB), low gain applications.