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In this manuscript, an optimal linear phase finite impulse response (FIR) filter is designed using water strider optimization algorithm and implemented in the field programmable gate array (FPGA). The initiative behind the linear phase FIR filter design is “to estimate the coefficients of optimum filter.” Here, the water strider optimization algorithm is proposed to evaluate the optimal filter coefficients (LPFIR-WSOA filter). The proposed LPFIR-WSOA filter attains 32.57, 19.09, 28.07, 27.42, 24.91 and 12.72% lower maximum pass ripple compared with the existing linear phase FIR filter. Finally, the proposed LPFIR-WSOA filter is implemented in FPGA for real-time application with the target families of Virtex 6 and Virtex 7. For target FPGA families Virtex 6, the FPGA-LPFIR-WSOA filter provides 16.7910, 15.074 and 18.065% lower maximum clock frequency (MHz); 62.3837, 41.9554 and 56.078% lower delay; and 23.7172, 20.324 and 26.417% lower memory usage compared with the existing LPFIR filters like global best steered quantum-inspired cuckoo search algorithm in FPGA (FPGA-FIR-GQICSA), modified artificial bee colony optimization-based FIR filter design in FPGA (FPGA-FIR-MABCO) and hybrid artificial bee colony algorithm-based FIR filter design in FPGA (FPGA-FIR-HABCA), respectively.

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

In traditional Stripmap SAR imaging, the platform motion error will bring the phase error in the azimuthal direction to the image, which will have a series of effects on the imaging quality. The traditional autofocus algorithm—Stripmap Phase Gradient Algorithm (SPGA)—can estimate any order phase error above the second order in theory, but it is difficult to estimate the linear phase error, which leads to the discontinuity of the estimated phase error. It usually needs multiple iterations to focus an image, which is inefficient. Moreover, because the linear phase error cannot be estimated, the traditional SPGA cannot eliminate the target offset in the image, resulting in the distortion of the image in the azimuthal direction. According to the continuity of phase error, we propose a modified iteration-free SPGA based on removing the linear phase. Without iteration, the proposed autofocus algorithm can achieve comparable or even better results than traditional SPGA. In the simulation experiments, piecewise linear errors are added to the images of multiple targets. SPGA still fails to focus the image after six iterations. The average ILSR and ILSR are −7.11 dB and −3.99 dB, respectively, and the average number of point target drift is 8.42 pixels. The proposed algorithm optimizes the average ILSR and ILSR to −12.34 dB and −9.87 dB and reduces the average number of point target drift to 0.16 pixels. In the actual data processing, using image entropy as the evaluation criterion, the time consumption is only 19.25% of SPGA under the condition of achieving the same focusing quality.

In existing global navigation satellite system-interference reflectometry (GNSS-IR) research, only the frequency of signal-to-noise ratio (SNR) oscillations has been used to estimate sea-level height. However, the characteristic parameters of SNR oscillations are not isolated from each other, and a single feature cannot accurately and comprehensively capture the environmental changes of reflecting surface. Our simulation results show that for the nonlinear least squares (NLS), when there is a certain difference between the fitting frequency and the actual frequency of SNR oscillations, the deviation of the phase solution obtained is approximately linear with the frequency difference. Consequently, a linear phase correction GNSS-IR sea-level estimation method is constructed in this study. This method integrates the Lomb–Scargle periodogram (LSP) and NLS to process SNR oscillations, using the phase obtained from NLS to correct the retrieval error of LSP. Through processing SNR data from four sites for nearly half a year, we verified the stability of the relationship between phase and frequency-based retrieval error at different sites in continuous monitoring, and established the relationship model between the two. Then, utilizing the relationship model acquired at different sites, we estimated the sea-level variations for the next 6 months at each site through joint frequency and phase versus reflector height relationships. Experimental results show that the phases acquired from NLS can effectively correct the retrieval error of LSP. Compared with the traditional method using only frequency, the root mean square error and mean absolute error of the retrieval results obtained from the linear phase correction GNSS-IR sea-level estimation method based on LSP-NLS are both reduced by about 60%. This multi-feature fusion technique introduces a new perspective and technical approach for GNSS-IR sea-level estimations.

Carbon fiber-reinforced polymers (CFRP) are extensively used in aerospace applications. Out-of-plane wrinkles frequently occur in aerospace CFRP parts that are commonly large and complex. Wrinkles acting as failure initiators severely damage the mechanical performance of CFRP parts. Wrinkles have no significant acoustic impedance mismatch, reflecting weak echoes. The total focusing method (TFM) using weak reflection signals is vulnerable to noise, so our primary work is to design discrete-time filters to relieve the noise interference. Wrinkles in CFRP composites are geometric defects, and their direct detection requires high spatial precision. The TFM method is a time-domain delay-and-sum algorithm, and it requires that the time information of filtered signals has no change or can be corrected. A linear phase filter can avoid phase distortion, and its filtered signal can be corrected by shifting a constant time. We first propose a wrinkle detection method using linear phase FIR-filtered ultrasonic array data. Linear phase filters almost do not affect the wrinkle geometry of detection results and can relieve noise-induced dislocation. Four filters with different bandwidths have been designed and applied for wrinkle detection. The 2 MHz bandwidth filter is recommended as an optimum choice.

Multi-h continuous phase modulation (CPM), with extremely high spectral efficiency, involves the plague of high demodulation complexity with a large number of matched filters and a complex trellis. In this paper, an efficient all-digital demodulator for multi-h continuous phase modulation (CPM) is proposed based on a low-complexity decision-directed synchronization algorithm. Based on the maximum-likelihood estimation of the carrier phase and timing errors, we propose a reduced-complexity timing error detector with linear phase approximation (LPA) to the phase of the multi-h CPM. Compared with the traditional synchronization methods, it avoids derivative matched filtering and reduces about 2/3 of matched filters. The estimated accuracy and bit error rate (BER) performance of the LPA-based synchronization algorithm have no loss, as shown by the numerical simulation. Its stability is verified by the derived S-curve. Then, the receivers with the LPA-based synchronization for the three kinds of promising multi-h CPM are implemented on a Xilinx Kintex-7 FPGA platform. The experimental results show that the onboard tested BER of the proposed design has an ignorable loss in the numerical simulation. The implementation overhead on FPGA is significantly reduced by about 27% slices, 64% DSPs, and 70% block RAMs compared with the conventional method.

The Hilbert transformation for generating the analytic signal or signal envelope is widely used in modern communication receivers, in radar and sonar systems. It introduces a 90 ∘  phase shift of the input signal. Since the impulse response of the ideal Hilbert transformer is non-causal, it must be approximated by an FIR or IIR filter. This paper shows results of novel algorithms for designing broadband digital IIR Hilbert transformers and its implementation. The designs employ Galerkin or collocation techniques. The transfer function of the Hilbert transformer is a rational polynomial of low order and exhibits approximately linear phase. The filters match the 90 ∘  phase shift requirement of Hilbert transformers almost perfectly and exhibit approximately constant group delay in the passband. The achieved image rejection ratio is typically larger than 50 dB. The quantization of the filter coefficients is realized by a Canonical Signed Digit (CSD) representation, reducing the hardware resources compared with two’s complement. The resulting filters are multiplier-less, which is crucial for high-speed signal processing and low power consumption. The design techniques and the CSD representation are realized in a MATLAB toolbox. The filters were moreover implemented in VHDL and SystemC. Additionally, a MATLAB tool for automatically generating a VHDL package containing the filter parameters has been implemented.

In this paper, a new design approach of approximately linear phase infinite impulse response (IIR) low pass digital differentiator (LPDD) is proposed and studied. The proposed design is based on a transfer function that has a numerator with anti-symmetric coefficients. To better control the magnitude response of the designed LPDD, the differential evolution (DE) optimization algorithm is used to find the coefficients of the transfer function that meets an appropriate pass band and stop band edge frequencies. The use of appropriate pass band and stop band edge frequencies gives the designer of the LPDD direct control on the width of the transition band. The designed LPDD using the proposed approach has approximately linear phase and much better magnitude response than that of the IIR LPDDs designed using other techniques reported in literature. In addition, the designed LPDD using the proposed approach has steeper roll-off magnitude response and narrower transition band than that of designed IIR and high order FIR LPDDs available in the literature.

The continuous wave interferences (CWIs) and the narrow-band interferences (NBIs) have significantly impacted the acquisition, tracking and positioning accuracy of Beidou Navigation Satellite System (BDS) receivers. As an interference suppression technology with a simple structure and low hardware cost, the adaptive infinite-duration impulse response (IIR) notch filter has been widely employed in the receivers to mitigate the CWIs and the NBIs. However, the nonlinear phase characteristics introduced by the IIR notch filters into the navigation receivers, may cause the distortion of navigation signals. It also leads to amplitude and phase distortion of the correlation peak in acquisition and loop tracking, which consequently brings on positioning errors in the measurement domain. This problem, however, has been ignored by many previous papers. Meanwhile, some other researchers came up with the idea of equalizers and all-pass networks compensating the distortion, which is also highly infeasible. Therefore, we propose a new method of an adaptive linear phase IIR notch filter with low hardware cost which is composed of three parts—the complex IIR notch filters, the IIR linear phase structure, and the adaptive and variable step-size algorithms. Applying this method, interference suppression and the correlation peak distortion compensation can be achieved with a modest increase hardware cost. This paper compares the performance of the new method with other IIR filters in both CWI and NBI scene and presents the effects of its parameters on the anti-jamming performance. Simulation results show that the proposed module has better anti-jamming performance in NBI scene and can compensate for the correlation peak distortion in the meantime.

From the perspective of the differential phase delay experienced by the two counterpropagating optical fields, the self-starting of the mode-locked fiber laser with a non-linear amplifying loop mirror (NALM) is theoretically studied. Although it is generally believed that NALM shows a saturable absorption effect on both continuous wave (CW) light and pulses, we find a counter-intuitive fact that cross-phase modulation (XPM) leads to opposite signs of differential non-linear phase shifts (NPSs) in these two cases, resulting in inverse saturable absorption (ISA) during the pulse formation process. The ISA is not helpful for the self-starting of laser mode-locking and can be alleviated by introducing a non-reciprocal phase shifter into the fiber loop. These results are helpful for optimizing the design of NALM and lowering the self-starting threshold of the high-repetition-rate mode-locked fiber laser.