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

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6246
Author(s):  
Dongxiao Wang ◽  
Xiaoqin Liu ◽  
Xing Wu ◽  
Zhihai Wang
Keyword(s):  
Signal Reconstruction ◽  
Sampling Rate ◽  
Sampling Theorem ◽  
Drive System ◽  
Reconstruction Method ◽  
Robot Arm ◽  
Reconstructed Signal ◽  
Band Limited ◽  
Simulation Signal ◽  
Important State

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.

On Derivative Sampling From Image Blur for Reconstruction of Band-Limited Signals

2014 ◽  
Author(s):  
Jacopo Tani ◽  
Sandipan Mishra ◽  
John T. Wen
Keyword(s):  
Numerical Study ◽  
Signal Reconstruction ◽  
Sampling Theorem ◽  
Image Sensors ◽  
Blurred Image ◽  
Derivative Sampling ◽  
Time Averages ◽  
Image Blur ◽  
Band Limited ◽  
Exposure Windows

Image sensors are typically characterized by slow sampling rates, which limit their efficacy in signal reconstruction applications. Their integrative nature though produces image blur when the exposure window is long enough to capture relative motion of the observed object relative to the sensor. Image blur contains more information on the observed dynamics than the typically used centroids, i.e., time averages of the motion within the exposure window. Parameters characterizing the observed motion, such as the signal derivatives at specified sampling instants, can be used for signal reconstruction through the derivative sampling extension of the known sampling theorem. Using slow image based sensors as derivative samplers allows for reconstruction of faster signals, overcoming Nyquist limitations. In this manuscript, we present an algorithm to extract values of a signal and its derivatives from blurred image measurements at specified sampling instants, i.e. the center of the exposure windows, show its application in two signal reconstruction numerical examples and provide a numerical study on the sensitivity of the extracted values to significant problem parameters.

An Effective LFM Signal Reconstruction Method for Signal Denoising

2018 ◽  
Vol 27 (09) ◽  
pp. 1850140
Author(s):  
Shan Luo ◽  
Guoan Bi ◽  
Tong Wu ◽  
Yong Xiao ◽  
Rongping Lin
Keyword(s):  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Experimental Results ◽  
Signal Denoising ◽  
Reconstruction Method ◽  
Signal To Noise ◽  
Time Frequency ◽  
Effective Time ◽  
Reconstructed Signal

One of the main challenges in signal denoising is to accurately restore useful signals in low signal-to-noise ratio (SNR) scenarios. In this paper, we investigate the signal denoising problem for multi-component linear frequency modulated (LFM) signals. An effective time-frequency (TF) analysis-based approach is proposed. Compared to the existing approaches, our proposed one can further increase the noise suppressing performance and improve the quality of the reconstructed signal. Experimental results are presented to show that the proposed denoising approach is able to effectively separate the multi-component LFM signal from the strong noise environments.

Image Reconstruction with the Fourier Coefficients for Magnetic Induction Tomography

2020 ◽  
Vol 16 (2) ◽  
pp. 156-163
Author(s):  
Jingwen Wang ◽  
Xu Wang ◽  
Dan Yang ◽  
Kaiyang Wang
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Magnetic Induction ◽  
Fourier Coefficients ◽  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Measurement Equation ◽  
Image Reconstruction Method ◽  
Magnetic Induction Tomography

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

scholarly journals Compressive sensing-based vibration signal reconstruction using sparsity adaptive subspace pursuit

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879087 ◽  
Author(s):  
Lin Zhou ◽  
Qianxiang Yu ◽  
Daozhi Liu ◽  
Ming Li ◽  
Shukai Chi ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Data Storage ◽  
Wireless Sensors ◽  
Signal Reconstruction ◽  
Estimation Method ◽  
Vibration Signal ◽  
Estimation Accuracy ◽  
Offshore Structure ◽  
Vibration Signals ◽  
Reconstructed Signal

Wireless sensors produce large amounts of data in long-term online monitoring following the Shannon–Nyquist theorem, leading to a heavy burden on wireless communications and data storage. To address this problem, compressive sensing which allows wireless sensors to sample at a much lower rate than the Nyquist frequency has been considered. However, the lower rate sacrifices the integrity of the signal. Therefore, reconstruction from low-dimension measurement samples is necessary. Generally, the reconstruction needs the information of signal sparsity in advance, whereas it is usually unknown in practical applications. To address this issue, a sparsity adaptive subspace pursuit compressive sensing algorithm is deployed in this article. In order to balance the computational speed and estimation accuracy, a half-fold sparsity estimation method is proposed. To verify the effectiveness of this algorithm, several simulation tests were performed. First, the feasibility of subspace pursuit algorithm is verified using random sparse signals with five different sparsities. Second, the synthesized vibration signals for four different compression rates are reconstructed. The corresponding reconstruction correlation coefficient and root mean square error are demonstrated. The high correlation and low error result mean that the proposed algorithm can be applied in the vibration signal process. Third, implementation of the proposed approach for a practical vibration signal from an offshore structure is carried out. To reduce the effect of signal noise, the wavelet de-noising technique is used. Considering the randomness of the sampling, many reconstruction tests were carried out. Finally, to validate the reliability of the reconstructed signal, the structure modal parameters are calculated by the Eigensystem realization algorithm, and the result is only slightly different between original and reconstructed signal, which means that the proposed method can successfully save the modal information of vibration signals.

Sampling-rate restrictions for exponential signal reconstruction

1972 ◽  
Vol 60 (6) ◽  
pp. 726-726 ◽  
Author(s):  
F.W. Fairman ◽  
R.D. Gupta
Keyword(s):  
Signal Reconstruction ◽  
Sampling Rate
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