Sub-Nyquist Sampling: Bridging Theory and Practice

Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely-tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous ShannonNyquist theorem has become a landmark: a mathematical statement which has had one of the most profound impacts on industrial development of digital signal processing (DSP) systems. Over the years, theory and practice in the field of sampling have developed in parallel routes. Contributions by many research groups suggest a multitude of methods, other than uniform sampling, to acquire analog signals [1]–[6]. The math has deepened, leading to abstract signal spaces and innovative sampling techniques. Within generalized sampling theory, bandlimited signals have no special preference, other than historic. At the same time, the market adhered to the Nyquist paradigm; state-of-the-art analog to digital conversion (ADC) devices provide values of their input at equalispaced time points [7], [8]. The footprints of Shannon-Nyquist are evident whenever conversion to digital takes place in commercial applications. Today, seven decades after Shannon published his landmark result in [9], we are witnessing the outset of an interesting trend. Advances in related fields, such as wideband communication and radio-frequency (RF) technology, open a considerable gap with ADC devices. Conversion speeds which are twice the signal’s maximal frequency component have become more and more difficult to obtain. Consequently, alternatives to high rate sampling are drawing considerable attention in both academia and industry.