Important state parameters, such as torque and angle obtained from the servo control and drive system, can reflect the operating condition of the equipment. However, there are two problems with the information obtained through the network from the control and drive system: the low sampling rate, which does not meet the sampling theorem and the nonuniformity of the sampling points. By combing equivalent sampling and nonuniform signal reconstruction theory, this paper proposes a reconstruction method for signal obtained from servo system in periodic reciprocating motion. Equivalent sampling combines the low rate and nonuniform samples from multiple periods into one single period, so that the equivalent sampling rate is far increased. Then, the nonuniform samples with high density are further resampled to meet the reconstruction conditions. This step can avoid the amplitude error in the reconstructed signal and increase the possibility of successful reconstruction. Finally, the reconstruction formula derived from basis theory is applied to recover the signal. This method has been successfully verified by the simulation signal of the robot swing process and the actual current signal collected on the robot arm testbed.

Reconstruction of Periodic Band Limited Signals from Non-Uniform Samples with Sub-Nyquist Sampling Rate.

In this paper, we propose a reconstruction approach for a multiple-sinusoidal signal. The signal reconstruction requires a small number of samples and is based on a sub-Nyquist sampling scheme with dual rate channels. In the proposed sampling scheme, the samples are grouped into multiple cosets. To obtain enough different cosets to reconstruct a signal, the sampling rates of channels are required to be relative coprime. For each coset, the Whittaker-Shannon interpolation formula is employed to construct the relation between the sub-Nyquist samples and the original signal, which is used to construct the measurement matrix. Since the multiple-sinusoidal signal is sparse in the frequency domain, compressed sensing theory can be adopted to reconstruct the signal. Simulation results are reported to demonstrate the feasibility and effectiveness of the proposed approach.

Compressed sensing based sub-Nyquist sampling of multiple sinusoids with dual rate channels

High resolution and wide swath, which are related to imaging quality and observation efficiency, are the key specifications for spaceborne synthetic aperture radar (SAR). Owing to the restrictions of the Nyquist sampling theorem, it is difficult to improve both specifications simultaneously. The increase of the swath width often leads to the decrease of the spatial resolution, e.g., in scanning SAR and terrain observation with progressive scan SAR. For a sparse scene, an image containing only a few targets has massive data but little useful information. This paper proposes a novel SAR observation mode, AgileSAR, which is based on the time–space sampling method and can overcome the limitations of the Nyquist theorem. It also increases the swath width while preserving the resolution of the sparse scene. AgileSAR steers the antenna beam towards a different sub-swath, generally after one or two pulse intervals, and the average pulse repetition rate corresponding to every sub-swath is much lower than that determined by the Nyquist theorem. Compared with Sentinel-1, which can achieve 5-m resolution and 80-km swath, a single azimuth-channel AgileSAR system can achieve 5-m resolution and 300-km swath for a sparse scene, once the corresponding system parameters are designed. The $\text{l}_{1}$ relaxation method is used to reconstruct sparse SAR images, and the reconstruction performance is quantitatively analyzed based on the estimation error. The simulation results validating the proposed method with sub-Nyquist samples can achieve approximately similar performance as conventional SAR with Nyquist samples.

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AgileSAR: Achieving Wide-Swath Spaceborne SAR Based on Time-Space Sampling

Compressive sensing has the ability of reconstruction of signal/image from the compressive measurements which are sensed with a much lower number of samples than a minimum requirement by Nyquist sampling theorem. The random acquisition is widely suggested and used for compressive sensing. In the random acquisition, the randomness of the sparsity structure has been deployed for compressive sampling of the signal/image. The article goes through all the literature up to date and collects the main methods, and simply described the way each of them randomly applies the compressive sensing. This article is a comprehensive review of random acquisition techniques in compressive sensing. Theses techniques have reviews under the main categories of (1) random demodulator, (2) random convolution, (3) modulated wideband converter model, (4) compressive multiplexer diagram, (5) random equivalent sampling, (6) random modulation pre-integration, (7) quadrature analog-to-information converter, (8) randomly triggered modulated-wideband compressive sensing (RT-MWCS).

Random Acquisition in Compressive Sensing: A Comprehensive Overview

Memory depth represents an oscilloscope's capability to continuously acquire and store sampling points at the highest real-time sampling rate. Improving the memory depth is conducive to improving the system's capability to analyze waveform details, but it will slow down the response time of the system. This paper proposes a high-speed deep memory data acquisition system with a real-time sampling rate of up to 10 GSPS and a memory depth up to 1 Gpts based on ultra-high-speed parallel sampling, waveform quick positioning and zooming, and waveform 3D mapping and display. This study focuses on the use of waveform quick positioning and zooming techniques under deep memory conditions to solve the slow response time and low waveform capture rate that are the result of improving the memory depth. This paper gives the experimental results for real-time signal data acquisition. The results show that adopting waveform quick positioning and zooming techniques achieved the following aims: significantly improved system response time, rapid positioning and display waveform details available to users, fast waveform capture rate and improved oscilloscope performance.

Waveform quick positioning and zooming techniques for a faster response time mass storage data acquisition system.

The random equivalent sampling (RES) is a sampling approach that can be applied to capture high speed repetitive signals with a sampling rate that is much lower than the Nyquist rate. However, the uneven random distribution of the time interval between the excitation pulse and the signal degrades the signal reconstruction performance. For sparse multiband signal sampling, the compressed sensing (CS) based signal reconstruction algorithm can tease out the band supports with overwhelming probability and reduce the impact of uneven random distribution in RES. In this paper, the mathematical model of RES behavior is constructed in the frequency domain. Based on the constructed mathematical model, the band supports of signal can be determined. Experimental results demonstrate that, for a signal with unknown sparse multiband, the proposed CS-based signal reconstruction algorithm is feasible, and the CS reconstruction algorithm outperforms the traditional RES signal reconstruction method.

Multiband signal reconstruction for random equivalent sampling.

Compressed sensing (CS) based sampling techniques exhibit many advantages over other existing approaches for sparse signal spectrum sensing; they are also incorporated into non-uniform sampling signal reconstruction to improve the efficiency, such as random equivalent sampling (RES). However, in CS based RES, only one sample of each acquisition is considered in the signal reconstruction stage, and it will result in more acquisition runs and longer sampling time. In this paper, a sampling sequence is taken in each RES acquisition run, and the corresponding block measurement matrix is constructed using a Whittaker-Shannon interpolation formula. All the block matrices are combined into an equivalent measurement matrix with respect to all sampling sequences. We implemented the proposed approach with a multi-cores analog-to-digital converter (ADC), whose ADC cores are time interleaved. A prototype realization of this proposed CS based sequential random equivalent sampling method has been developed. It is able to capture an analog waveform at an equivalent sampling rate of 40 GHz while sampled at 1 GHz physically. Experiments indicate that, for a sparse signal, the proposed CS based sequential random equivalent sampling exhibits high efficiency.

Sequential time interleaved random equivalent sampling for repetitive signal.

Compressive sensing (CS) aims at decreasing sampling rate to reduce the needed number of samples. On the other hand, the one-bit CS is proposed to reduce the quantization bit. In this paper, we proposed a one-bit CS system aiming at acquiring the multiband sparse signal which is a very popular signal model in wireless communication, especially in cognitive radio. This proposed system, called direct one-bit sampler (DOS), is simple in hardware implementation, and it consists of only a comparator working at Nyquist rate. In the stage of signal reconstruction, it can be equivalent to a special multicoset sampler which is a popular scheme in CS. Moreover, we propose an enhanced binary iterative hard thresholding (BIHT), a popular one-bit recovery algorithm, to deal with the multiple measurement vectors in the one-bit CS framework. Both the theoretical model and experimental results demonstrate that the proposed DOS, with the help of the enhanced BIHT, can not only accurately recover the positions of active subbands of the multiband sparse signal but also roughly estimate the power of each active subband.

Multiband sparse signal reconstruction through direct one-bit sampling.

A sub-Nyquist coprime sampling system for sparse signals is implemented in this article. The proposed system is composed of coprime sampling hardware and a multicoset signal reconstruction algorithm. A pair of uniform samplers is utilized in the hardware to sample a wideband spare analog signal with an uncertain difference in start times. A time difference acquisition module embedded into a field-programmable gate array and a pulse-expanding circuit are then used to measure the difference in start times. Owing to the different frequencies of the two samplers, the coprime sample sets obtained are nonuniform. Before they are used as input to the multicoset signal reconstruction algorithm, these coprime sample sets need to be regrouped into multicoset sample sets according to the sample pattern. The results of experiments indicate that the signals can be reconstructed at an equivalent rate of the order of gigahertz from sub-Nyquist samples acquired by the designed coprime acquisition system.

Yijiu Zhao

Papers

Multiband signal reconstruction for random equivalent sampling.

Sequential time interleaved random equivalent sampling for repetitive signal.

Multiband sparse signal reconstruction through direct one-bit sampling.

GHz sampling hardware implementation with sub-Nyquist coprime sampling rates.