In this study, the authors modify the mapping function by introducing a non-linear term based on Riemann–Liouville definition of fractional derivatives and its application to the mean squared error in addition to the first-order partial derivatives; thus create fractional variants of the least mean square (LMS) algorithm and its normalised version. The introduction of fractional term helps increase the convergence rate through the non-linear update term which depends on the fractional order and the in-process LMS weights; for steep gradient of the error measure, large changes are made to the weights which help the equaliser filter to better track the effects of multipath fading channels. They verify and validate the working of the proposed technique in the decision feedback equalisation of multipath fading channels for higher-order quadrature amplitude modulations; comparative results are shown in terms of performance metrics as symbol-error rate for various fractional orders and step sizes, combined equaliser and channel responses for different number of training symbols; simulations show that the proposed approach outperforms the conventional counterpart.

This study proposes an optimised algorithm to remove power line interference (PLI) from electrocardiogram (ECG) signal based on ensemble empirical mode decomposition (EEMD). A computationally efficient algorithm is one of the important requirements for real-time monitoring of cardio activities and diagnosis of arrhythmias. Computational complexity in EEMD is significantly reduced by using the EMD as the preprocessing stage. The noisy ECG signal is decomposed into intrinsic mode functions (IMFs) using EMD. ECG signals which are affected by PLI are automatically identified based on the simple ratio of the zero crossing number of IMF components. EEMD is used to decompose only ECG segments constructed from the noisy IMF components. The proposed algorithm is evaluated by real ECG signals available in MIT-BIH arrhythmia database in terms of signal-to-noise ratio and root mean square error. The computational efficiency of this new framework is measured using MATLAB profiling functions and compared with EMD, EEMD, sign-based adaptive and EMD with wavelet-based methods. Results show that the proposed algorithm performs better than the EMD, EEMD, sign-based adaptive and EMD with wavelet-based methods and it is computationally more efficient than EMD and EEMD methods.

This study addresses the problem of tracking extended target with intermittent observations. Based on practical applications, two Bernoulli distributed random variables are employed to describe the intermittent phenomenon of the positional measurements and the measurements of target extent, respectively. First, a machine vision algorithm is developed to solve the target shape parameters. Then, four sub-filters are designed according to the received observations and the achieved target shape parameters. The output of the proposed tracking filer can be obtained by the weighted-confidence fusion of the sub-filters. Finally, the machine vision algorithm is evaluated by the virtual target images created in OpenGL (Open Graphics Library) and the real images of a moving ship. The performance of the designed tracking filter is compared with the traditional tracking filter. The experiment results show the effectiveness of the machine vision approach; also the Monte-Carlo runs demonstrate that the provided tracking filter outperforms the traditional one with respect to accuracy.

Despite the large bandwidth available for all users in high-speed wireless networks, resources allocation and user scheduling remain essential to combat interference, increase throughput and reduce complexity. As the number of users increases, the computational complexity tends to increase significantly. The trade-off between the complexity reduction and capacity improvement is the challenge. Hence a unique ant-colony optimisation method is implemented with successive interference cancellation to reduce complexity and provide higher capacity to more users. The incurred complexity is at least 50% less than other schemes. The average mean square error achieved is around 4 dB smaller than that of the existing scheme.

Blind image deblurring is an important topic which is widely used in many research fields such as photography, optics, astronomy, medical images, monitoring, military and so on. Although many algorithms have been proposed to improve the deblurring result in the past years, most of them cannot perform perfectly in some challenging cases. This study presents a novel blind deblurring method based on an adaptive weighted total variation (TV) algorithm. The blur kernel estimation is based on the image structure, the sparsity and continuity prior of point spread function is also taken into account. To get better effect of removing the ringing artefacts, adaptive weight calculated according to the property of the higher-order partial derivatives in the local image is proposed in TV algorithm to alleviate the ill-posed inverse problem and stabilise the solution for latent image restoration. The experimental results prove that the proposed algorithm can suppress the ringing artefacts to a great extent in the latent image, and can get much better effect in both vision and theoretical results than traditional algorithms.

In this study, a non-linear filtering algorithm for state estimation with symmetric alpha-stable (SαS) noise is presented. The dynamic system model investigated here can be described by a linear state-space equation and a non-linear observation equation. The contribution of this study can be summarised as follows. First, particle filtering approach is employed for coarse estimation of the unknown parameters and then Kalman filter is performed to achieve better estimation. Second, SαS noise is considered as the additive disturbance in the observed signal and Gaussian approximation is used to compute the characteristics. Third, the calculation complexity is analysed according to the proposed algorithm. The proposed method is compared with the standard particle filter, extended Kalman filter and unscented Kalman filter for static parameter estimation of a periodic signal. As a practical application, the proposed method is used in high frequency source localisation based on time difference of arrival measurements.

As a data-driven, equation-free decomposition method, the DMD can characterise dynamic behaviour of a non-linear system by using the DMD modes and eigenvalues. However, all current provable algorithms suffer from a separate procedure for obtaining the DMD modes and determining the number of modes. In this study, the authors propose a nuclear norm regularised DMD (NNR-DMD) algorithm that produces low-dimensional spatio-temporal modes. A nuclear norm regularisation term is added to the optimisation problem of the standard DMD algorithm for prompting the sparsity of the projected DMD modes. Split Bregman method is applied to solve the regularised convex, but non-smooth optimisation problem. Several numerical examples demonstrate the potential of the proposed NNR-DMD algorithm: (i) it can identify the low-dimensional spatio-temporal DMD modes in which each of them possesses a single temporal frequency; (ii) the reconstruction errors based on the sparse DMD modes can be reduced when it compares with the sparsity-promoting DMD algorithm penalising the l ₁-norm of the vector of DMD amplitudes; and (iii) it can obtain low-dimensional coherent structures when the NNR-DMD algorithm is applied to coherency identification of generators in an interconnected power system.

An 8-point discrete cosine transform (DCT) fast algorithm based on the Loeffler DCT factorisation and algebraic integer (AI) representation is proposed. The proposed algorithm is an error-free implementation of the Loeffler algorithm and it is capable of computing the 8-point DCT multiplierlessly. Decoding architectures are also proposed for mapping AI encoded quantities back to usual fixed point arithmetic using canonical signed digit representation and the expansion factor method. The proposed algorithm is mapped into systolic-array digital architectures and physically realised as digital prototype circuits using field-programmable gate array technology on a Reconfigurable Open Architecture Computing Hardware board and mapped to 0.18 μm complementary metal–oxide–semiconductor technology using AMS Encounter Digital Implementation libraries at 1.8 V supply.

In the state-of-the-art single channel speech enhancement techniques, the short-time spectral amplitude is modified while the effect of the phase corruption due to the contamination of additive noise is neglected. This study introduces an improved speech enhancement algorithm based on a phase-aware multi-band spectral subtraction technique which estimates the spectral amplitude of the clean speech signal by considering the phase of the speech and noise signal components, and uses the estimated phase of the clean speech signal for signal reconstruction in the time domain. Experimental results show that the proposed algorithm yields better performance in terms of various objective and composite quality measures and other intelligibility assessment metrics while compared with other existing spectral subtraction methods. Using the composite objective measure quality evaluation technique, it is observed that the overall signal quality of the enhanced speech signal is improved on an average by 70% at 0 dB global input signal-to-noise ratio by using the proposed approach.

In this study, the authors focus on pulse modulation waveform estimation based on a sequence of intercepted pulses from the same radar emitter. In general, modulation waveform estimators first perform pulse alignment in time and frequency separately, and then accumulate the aligned pulses to estimate the waveform. However, commonly used alignment methods may lead to considerable alignment errors which are difficult to detect and compensate, especially under low signal-to-noise ratio (SNR) conditions, resulting in non-ideal effects of accumulation. This study proposes a robust and nearly optimal modulation waveform estimation algorithm. The new algorithm first aligns pulses in time and frequency jointly via the cross-ambiguity function to avoid the transfer and accumulation of alignment errors. After that, an iterative maximum-likelihood estimator is invoked to achieve the waveform estimation. Theoretical analysis and extensive experiments show that the proposed algorithm has much smaller alignment errors and better modulation waveform and modulation parameter estimation ability than competing methods at low SNRs, and can approach the ideal case. Moreover, this algorithm does not make any assumption on the type of modulation and is computationally efficient, thus having broad applications.

Adaptive notch filters have been the focus of intense research for more than three decades. Low computational requirements and good performance make them attractive for tracking frequency modulated signals. Despite the extensive literature on adaptive notch filters, algorithm extensions and new models for describing the dynamics of the notch frequency continue to be proposed. In this study, the equivalence between adaptive notch filters using a plain gradient (PG) algorithm and frequency lock loops (FLLs) with exponential filtering is established. FLL theory is then used to analyse the noise performance and signal tracking capabilities of adaptive notch filters. A linear model describing the dynamics of the filter adaptation process is derived and the concepts of loop and Doppler bandwidths are introduced. Criteria based on the loop and Doppler bandwidths are suggested to set the PG adaptation step. Finally, algorithm extensions based on the FLL theory are proposed. Theoretical results are supported by Monte Carlo simulations which show the validity of the analysis performed.

In this study, the lifting scheme is first employed to design two-channel biorthogonal graph filter bank. The biorthogonal condition is parameterised by imposing a single-level lifting structure on the analysis and synthesis graph kernels. Based on the parametric structure, the two kernels are separately optimised by constrained quadratic programming. The obtained two-channel biorthogonal graph filter banks are of structurally perfect reconstruction. Numerical results and comparison are included to show the proposed algorithm can lead to biorthogonal graph filter banks with improved performance.

Adaptive decision feedback equalisers (ADFEs) are used in wireless transmission systems for mitigating the InterSymbol Interference (ISI) that occurs due to multipath propagation of the transmitted signal. In case of high speed communications which involve rapid-varying channels, fast convergent and low complexity ADFEs are required. Frequency domain block processing of signals is an effective means of handling the increased complexities in such high speed systems. However, block ADFEs being inherently non-causal, the feedback filter (FBF) suffers from the lack of unknown decisions in every block computation. In this study, the authors propose an efficient approach for the computation of these unknown decisions. For this, the authors tried to minimise a cost function based on two criteria mean-absolute difference (MAD) and mean-square difference between the ADFE output and the adder that sums up the feedforward filter (FFF) and FBF. A bank of registers which store all the symbols used in the modulation scheme is also utilised for this purpose. Using the proposed solution, the authors recast block ADFE equations in the frequency domain using distributed arithmetic (DA). The algorithm has a good convergence performance and utilises only few computations compared with the existing schemes.

State-of-the-art speech representations provide acceptable recognition results under optimal conditions, though their performance in adverse conditions still needs to be improved. In this direction, many advances involving wavelet processing have been reported, showing significant improvements in classification performance for different kinds of signals. However, for speech signals, the problem of finding a convenient wavelet-based representation is still an open challenge. This study proposes the use of a multi-objective genetic algorithm for the optimisation of a wavelet-based representation of speech. The most relevant features are selected from a complete wavelet packet decomposition in order to maximise phoneme classification performance. Classification results for English phonemes, in different noise conditions, show significant improvements compared with well-known speech representations.

The measurement of optical fibre vibration is a key part of optic fibre pre-warning system, which has gradually focused on phase-sensitive optical time-domain reflectometer. However, for this instrument, false alarm rate is very high and some unstable intrusion signals cannot be detected by using its fixed threshold method in the actual application. It needs to develop new vibration detection method to overcome the above defect. The vibration signals normally consist of three parts, that is, noise, interference and intrusion signals. After a large number of data analysis, the authors find that the system noise is time varying and follows the Rayleigh distribution. Hence, the authors innovatively use the constant false alarm rate (CFAR) method to detect this type of intrusion. Considering interference is also time varying and diverse, a good detection performance cannot be obtained only by using the conventional CFAR. For this reason, a background homogeneity adaptive CFAR (BHA-CFAR) method is further proposed to detect the vibration signals in this study. The BHA-CFAR consists of two detectors, cell averaging CFAR (CA-CFAR) detector and greatest-of/smallest-of CFAR (GO/SO-CFAR) detector. A parameter, homogeneity of background, is estimated first to classify the surrounding. Then CA-CFAR and GO/SO-CFAR are optionally used according to the surrounding is homogeneous or heterogeneous, respectively. This new detection method can adapt to any background surrounding and has a good detection performance. In order to check the feasibility and validity of the BHA-CFAR method, several experiments were carried out in Da Gang oilfield. The detection results show that the proposed method can provide a good tradeoff between the detection performance and computation time.

Motion errors are inevitably introduced when data is acquired and considerably degrade the image quality in terms of geometric resolution, radiometric accuracy and image contrast, especially in high-resolution spotlight synthetic aperture radar (SAR) imagery. In this study, the authors present a novel two-dimensional (2D) autofocus algorithm directly inserted into polar format algorithm, which compensates the envelop error and the phase error sequentially. A coarse error correction is first performed by global positioning system or inertial navigation system in the range-compressed domain, then a new envelop compensation strategy, stage-by-stage approach, is designed, obtaining promising results for removing range cell migration after 2D interpolation. Additionally, a weighed contrast enhancement autofocus algorithm based on spatially variant model is developed to compensate for the residual phase error, which remarkably improves the estimation accuracy. The presented algorithm is very robust to deal with substantial errors over a variety of scenes even in conditions of homogenous areas with no prominent point scatterers and enables the utilisation of fast Fourier transform. The experimental results obtained by the proposed algorithm confirm that the analysis extends well to realistic situations.