Zero‐crossing representation in the wavelet transform domain and signal reconstruction

We present a new stabilized zero-crossing representation with a salient feature that the signal reconstruction problem reduces to a typical minimum-norm optimization problem, the solution of which is formulated as a linear simultaneous equation, and develop an iterative algorithm for signal reconstruction. Moreover, we extend them to the two-dimensional case. With the extended two-dimensional reconstruction algorithm we can almost perfectly reconstruct an original image from the stabilized two-dimensional zero-crossing representation, and after some dozens of iterations the algorithm provides a reconstructed image with subjectively high picture quality. Furthermore, we introduce a threshold operation based on edge intensity to reduce the amount of information in the stabilized zero-crossing representation, and experimentally demonstrate that the threshold operation works well.

The development of wireless technology in recent years has increased the demand for channel resources within a limited spectrum. The system's performance can be improved through bandwidth optimization, as the spectrum is a scarce resource. To reconstruct the signal, given incomplete knowledge about the original signal, signal reconstruction algorithms are needed. In this paper, we propose a new scheme for reducing the effect of adding additive white Gaussian noise (AWGN) using a noise reject filter (NRF) on a previously discussed algorithm for baseband signal transmission and reconstruction that can reconstruct most of the signal’s energy without any need to send most of the signal’s concentrated power like the conventional methods, thus achieving bandwidth optimization. The proposed scheme for noise reduction was tested for a pulse signal and stream of pulses with different rates (2, 4, 6, and 8 Mbps) and showed good reconstruction performance in terms of the normalized mean squared error (NMSE) and achieved an average enhancement of around 48%. The proposed schemes for signal reconstruction and noise reduction can be applied to different applications, such as ultra-wideband (UWB) communications, radio frequency identification (RFID) systems, mobile communication networks, and radar systems.

Chapter 5 - Digital Signal Processing

A technique is presented for the reconstruction of signals that suffered sampling-frequency decimation. Two assumptions are made: the original signal has to be repetitive, and no anti-aliasing filter has been used before frequency decimation. The performance of the technique is assessed by using test signals of which the original signal is known.

The processing of radio occultation signals has the purpose of extracting the bending angle as function of the impact parameter so that a following Abel transform gives the refractivity profile of the atmosphere. The radio occultation signal is the detected electromagnetic field from a remote transmitter (a GPS satellite). Various processing techniques can be used to retrieve the bending angle. The Full Spectrum Inversion (FSI) method relies on geometrical optics and will produce the actual bending angle as function of the impact parameter, if it can be assumed that the refractivity is spherically symmetric around the Earth and the geometrical optical description of the propagating electromagnetic field is correct. The inverse problem, construction of the electromagnetic field from knowledge of the refractivity profile (or the bending angle) and the path of the receiving and transmitting antennas can also be solved in the framework of geometrical optics. This opens a way to evaluate the quality of actual occultation measurements both with respect to the computational algorithms and the assumptions of spherical symmetry. When the refractivity profile has been measured from an occultation signal, this profile together with information about the satellites’ path can be used to generate a simulated signal, which can be compared with the original signal. Processing of real data is shown here and the results are discussed.

In the compressive sampling theory, a small number of random linear projections of a sparse or compressible signal have contained sufficient information and the original signal can be accurately reconstructed by taking advantage of modern optimization algorithms. We proposed an approximate l 0 norm based signal reconstruction algorithm in this paper. It not only can convert the classical constrained l 0 minimization problem of the compressive sampling theory into an unconstrained optimization problem, but also can reduce the dimension of the search space substantially. The experiment results have shown that our proposed algorithm can improve the sparse signal reconstruction performance while maintaining appropriate signal reconstruction efficiency.

In addressing the problem of low prediction accuracy in the remaining useful life (RUL) prediction of rolling bearings, caused by noise interference and insufficient extraction of sensitive features by deep learning models, this paper presents a life prediction method based on signal reconstruction and dual-channel network fusion. First, addressing the issue of extracting weak features from rolling bearing vibration signals, an optimized combination of variational mode decomposition (VMD) and Teager–Kaiser energy operator (TKEO) for signal reconstruction is proposed. TKEO is used to track the energy of high-frequency impulses in the original signal. The sparrow search algorithm is employed for optimizing VMD to perform high-frequency filtering, resulting in an optimized impulse energy signal. This signal is then multiplied with the original signal to enhance weak impulse features under noisy background. Next, a dual-channel network model for RUL prediction is constructed based on temporal convolutional network (TCN) and convolutional neural networks (CNNs). The one-dimensional time-series signal obtained after reconstruction and denoising serves as the input for the TCN network channel. Simultaneously, the signal obtained after reconstruction and denoising undergoes synchrosqueezed wavelet transforms to generate a two-dimensional time–frequency representation as input for the CNN network channel. This setup allows TCN and CNN to respectively extract temporal features from the vibration signal and time–frequency features from the spectrogram. By incorporating self-attention mechanisms, internal correlations between different features are fully explored, thereby enhancing prediction accuracy.

Compressed sensing represents an interesting approach in signal processing and reconstruction. The theory involves a surprising number of branches of mathematics: linear algebra, functional analysis, convex and non-convex optimization, nonlinear approximation theory and probability. In general, the applications of compressed sensing can be found (or searched) wherever it is possible to express the signal in sparse representation in a “standard” base or in a base that was adjusted for particular signal. Core applications of compressed sensing today include image processing, signal denoising, image deblurring and inpainting. This paper addresses analysis the influence of external phenomena on the signal reconstruction using compressed sensing in wireless sensor networks. Such external phenomena include, for instance, additive white Gaussian noise (AWGN), attenuation or time shift. Three acoustic input signals sparse in frequency domain are used in experiments. The first one with significant frequency band from 500Hz up to 700Hz. The second signal with one significant frequency band from 2400Hz up to 3100Hz with considerable frequency bands between 0Hz to 1000Hz and 5000Hz to 6000Hz. The third signal used is a synthesized artificial sound invented for the experiment purposes only. It is strictly sparse in the frequency domain and has exactly three frequency bands between 400Hz and 500Hz, 2000Hz and 2100Hz, 9000Hz and 9100Hz. The results show that additive noise as well as attenuation have significant effect on the reconstruction accuracy using the selected distribution scenario and reconstruction method. On the other side, the time shift has no significant effect on the reconstruction.

An experimental study of mobile teletext reception is described. Teletext in Japan is a broadband signal with 5.73 Mb/s; therefore, multipath interference is a serious problem in mobile reception, and it is impossible to obtain the teletext correctly by conventional methods. A multipath reduction technique using signal processing in the frequency domain is developed. In this technique, an original chirp signal is used for reference to identify radio propagation paths. In field trials, the delay profile is precisely obtained, and the bit error rate can be reduced. the error correction capability is also tested in a computer simulation. The proposed method was found to improve the error rate when the signal-to-noise ratio was greater than 20 dB. >

This paper proposes a signal adaptive algorithm for multi-resolution analysis based on analytic signal matched filter bank (SMFB) to decompose time variant biomedical signals (e.g. ECG) into narrow bands such that each band has only one harmonic frequency component of the original ECG signal. Consecutively, maximum harmonic component present in the bio-signal is easily detected and the minimum number of harmonics required for estimated reconstruction of original ECG signal is obtained. The proposed scheme is exceedingly useful in transmission and reconstruction of bio-electric signal like ECG and can be valuable in treatment of patients in remote locations at reduced sub-band rate. As this technique can be used in near real-time classification from the ECG data as it arrives, which is evidenced by its time-frequency analysis, the system can be used as classifier as well as predictor for heart abnormalities such as Premature Ventricular Contractions (PVC).

This paper considers two-dimensional phase retrieval using a window function. First, we address the uniqueness and reconstruction of a two-dimensional signal from the Fourier intensities of the three signals: the original signal, the signal windowed by a window w(m,n) and the signal windowed by its complementary window w/sub c/(m,n)=1-w(m,n). Then we consider the phase retrieval without a complementary window. We develop conditions under which a signal can be uniquely specified from the Fourier intensities of the original signal and the windowed signal by w(m,n). We also present a reconstruction algorithm.

The necessity to process signals living in non-Euclidean domains, such as signals defined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes itself by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals decomposes in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange information only within its neighbor to perform a given filtering operation. Similarly to the classical filters, we propose ways to design and implement distributed finite impulse response and infinite impulse response graph filters. One of the key contributions of this thesis is to bring the temporal dimension to graph signal processing and build upon a graph-time signal processing framework. This is done in different ways. First, we analyze the effects that the temporal variations on the graph signal and graph topology have on the filtering output. Second, we introduce the notion of joint graph-time filtering. Third, we presentpr a statistical analysis of the distributed graph filtering when the graph signal and the graph topology change randomly in time. Finally, we extend the sampling framework from the reconstruction of graph signals to the observation and tracking of time-varying graph processes. We characterize the behavior of the distributed autoregressivemoving average (ARMA) graph filters when the graph signal and the graph topology are time-varying. The latter analysis is exploited in two ways: i ) to quantify the limitations of graph filters in a dynamic environment, such as a moving sensors processing a time-varying signal in a sensor network; and i i ) to provide ways for filtering with low computation and communication complexity time-varying graph signals. We develop the notion of distributed graph-time filtering, which is an operation that jointly processes the graph frequencies of a time-varying graph signal on one hand and its temporal frequencies on the other hand. We propose distributed finite impulse response and infinite impulse response recursions to implement a two-dimensional graphtime filtering operation. Finally, we propose design strategies to find the filter coefficients that approximate a desired two-dimensional frequency response. We extend the analysis of graph filters to a stochastic environment, i.e., when the graph topology and the graph signal change randomly over time. By characterizing the first and second order moments of the filter output, we quantify the impact of the graph signal and the graph topology randomness into the distributed filtering operation. The latter allows us to develop the notion of graph filtering in the mean, which is also used to ease the computational burden of classical graph filters. Finally, we propose a sampling framework for time-varying graph signals. Particularly, when the graph signal changes over time following a state-space model, we extend the graph signal sampling theory to the tasks of observing and tracking the time-varying graph signal froma few relevant nodes. The latter theory considers the graph signal sampling as a particular case and shows that tools from sparse sensing and sensor selection can be used for sampling.

For the bogie traction motor bearings of rail vehicles under road transportation conditions, its vibration signal full-time domain data acquisition data volume, storage pressure, subsequent data analysis difficulties, and other problems. This study proposes a data compression acquisition and data reconstruction method for bearing vibration signals based on compressed sensing (CS), which can achieve compressed sampling, transmission, and storage of the original signal with fewer observations, and restore the original signal by combining reconstruction algorithms to achieve low error reconstruction. We study the effects of different sparse transform methods on signal sparsity, as well as the signal sparse performance based on different sparse transforms and the signal reconstruction effect of different reconstruction algorithms, and propose a sparse representation method based on the discrete Fourier transform (DFT) and the generalized orthogonal matching pursuit (gOMP) algorithm for CS. Through simulation and experimental comparison, it is concluded that the method can restore and reconstruct the original high-dimensional signal with small reconstruction error, and solve the problems of massive data, inconvenient transmission, and difficult data analysis in engineering.

Performance study of online batch-based digital signature schemes

Precise time difference (time interval) measurement has been widely applied in communication, detection, and metrology. Among the various methods of time difference measurement, the analog zero-crossing detection method and the full digital processing methods are commonly used in ultrasonic flow measurement application. Conventional full digital processing methods, which take advantage of total signals’ waveforms, can have high accuracy in high signal to noise ratio (SNR) when employing a high enough sampling frequency and extremely high performance digital signal processors; but their accuracies are severely limited by the hardware costs and can be easily affected by the noise and the distortion of signals. As a viable method, the analog zero-crossing detection method can achieve high resolution, whose accuracy, however, is easily influenced by the detection threshold and baseline shifts of the received signals, as well as the noises. In this paper, the digital zero-crossing detection algorithm is proposed for ultrasonic flow measurement to achieve high-precision and high-robustness time difference estimation at relatively low hardware costs, i.e., a relatively low sampling rate (e.g., 10 Msamples/s) and a relatively low computational load. The digital zero-crossing detection algorithm is performed with the signal reconstruction and the least-square fitting technologies. The simulation and experiment results show that compared with conventional methods, the proposed method presents higher accuracy and higher robustness, especially in the case of low SNR.