Abstract
The pioneering steps taken toward digitization of signals can be attributed to the theoretical work done by Kotelnikov, Nyquist, Shannon and Whittaker on sampling continuous-time band-limited signals [87, 128, 160, 187].
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Notes
- 1.
Sampling a signal, in order to represent analog information (i.e. electromagnetic RF) in a digital form, is done by means of an analog-to-digital converter (ADC) [185]. Many variations of these electrical components exists, all sharing the same principle for acquisition but with varying techniques. Additionally, some exhibit benefits over others in terms of bit depth and/or sampling rate. The ADC types that exist and are widely used, include flash, sigma-delta, successive-approximation, ramp-compare, and pipeline [183]. Current ADCs are capable of a conversion rate of up to \(3.6 \ GSPS\) and a bit depth of 12 bits. However these ADCs, although fast, do come at a price that for conventional use in RF systems is exorbitantly high—in the range of > $4 000 per ADC, as of 2013 [76].
- 2.
ENOB refers to the effective number of bits and the SNDR denotes the signal to noise ratio + distortion ratio.
- 3.
Combinatorial techniques —developed by the theoretical computer science community [38]—utilize the count-min, count-median or Bayesian methods. Combinatorial algorithms assume that the origin of a signal of interest comes from a probability distribution, which imposes a belief of propagation on the recovery [20]; or modelled for data network [72] and probabilistic learning applications [79]. Thus, the relevance to our work—with exception to Fourier sampling in [64]—is minimal, and we leave it to the reader to explore further.
- 4.
F cost function penalizes the difference in terms of Euclidean distance between the \(\varPhi x\) and y in vector form [150].
- 5.
Distributed as open source code, written in Matlab and it can be accessed at [27].
- 6.
\(\lambda _{i}f_{i}=0 \), which converges subject to \(\lambda _{i}^{k}f_{i}(z^{k}) = -1/\tau ^{k}\) where the parameter \(\tau ^{k}\) is increased progressively in accordance to the Newton iterations [26].
- 7.
L1_LS source code (written in Matlab\(^{\copyright }\)) and can be accessed in [129].
- 8.
\(\ell _{1}-\)homotopy code can be accessed at [129].
- 9.
Software package for SpaRSA algorithm can be accessed in [129].
- 10.
Software package for FISTA algorithm can be accessed in [129].
- 11.
Software package for ALM algorithm can be accessed in [129].
- 12.
Software package for YALL1 algorithm can be accessed in [129].
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Mishra, A.K., Verster, R.S. (2017). Compressive Sensing: Acquisition and Recovery. In: Compressive Sensing Based Algorithms for Electronic Defence. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-46700-9_3
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DOI: https://doi.org/10.1007/978-3-319-46700-9_3
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