We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery ...is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erdös-Rényi graphs, random sampling leads to perfect recovery with high probability. We further establish the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs. To handle full-band graph signals, we propose a graph filter bank based on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification of online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to previous work.
We propose a processor based on the concatenation of two fractional temporal Talbot dispersive lines with balanced dispersion to perform the DFT of a repetitive electrical sequence, for its use as a ...controlled source of optical pulse sequences. The electrical sequence is used to impart the amplitude and phase of a coherent train of optical pulses by use of a modulator placed between the two Talbot lines. The proposal has been built on a representation of the action of fractional Talbot effect on repetitive pulse sequences and a comparison with related results and proposals. It is shown that the proposed system is reconfigurable within a few repetition periods, has the same processing rate as the input optical pulse train, and requires the same technical complexity in terms of dispersion and pulse width as the standard, passive pulse-repetition rate multipliers based on fractional Talbot effect.
•A DFT processor of repetitive sequences based on temporal Talbot effect is proposed.•The sequence is encoded as complex amplitudes of a pulse train by use of a modulator.•The modulator is placed between two fractional Talbot lines with matched dispersion.•The proposal is built from a linear transform representing fractional Talbot effect.•The system has the same complexity as passive pulse-repetition rate multipliers.
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the ...computational complexity of the reconstruction is exponential as it is. To overcome this difficulty, we extend the idea of compressed sensing, and propose to solve the problem by minimizing the sum of weighted absolute values. We assume that the probability distribution defined on an alphabet is known, and formulate the reconstruction problem as linear programming. Examples are shown to illustrate that the proposed method is effective.
We present a multiresolution classification framework with semi-supervised learning on graphs with application to the indirect bridge structural health monitoring. Classification in real-world ...applications faces two main challenges: reliable features can be hard to extract and few labeled signals are available for training. We propose a novel classification framework to address these problems: we use a multiresolution framework to deal with nonstationarities in the signals and extract features in each localized time-frequency region and semi-supervised learning to train on both labeled and unlabeled signals. We further propose an adaptive graph filter for semi-supervised classification that allows for classifying unlabeled as well as unseen signals and for correcting mislabeled signals. We validate the proposed framework on indirect bridge structural health monitoring and show that it performs significantly better than previous approaches.
With the rapid development of Connected and Automated Vehicle (CAV) technology, limited self-driving vehicles have been commercially available in certain leading intelligent transportation system ...countries. When formulating the car-following model for CAVs, safety is usually the basic constraint. Safety-oriented car-following models seek to specify a safe following distance that can guarantee safety if the preceding vehicle were to brake hard suddenly. The discrete signals of CAVs bring a series of phenomena, including discrete decision-making, phase difference, and discretely distributed communication delay. The influences of these phenomena on the car-following safety of CAVs are rarely considered in the literature. This paper proposes an efficient safety-oriented car-following model for CAVs considering the impact of discrete signals. The safety constraints during both normal driving and a sudden hard brake are incorporated into one integrated model to eliminate possible collisions during the whole driving process. The mechanical delay information of the preceding vehicle is used to improve car-following efficiency. Four modules are designed to enhance driving comfort and string stability in case of heavy packet losses. Simulations of a platoon with diversified vehicle types demonstrate the safety, efficiency, and string stability of the proposed model. Tests with different packet loss rates imply that the model could guarantee safety and driving comfort in even poor communication environments.
Sleep apnea is a disease that occurs due to the decrease in oxygen saturation in the blood and directly affects people's lives. Detection of sleep apnea is crucial for assessing sleep quality. It is ...also an important parameter in the diagnosis of various other diseases (diabetes, chronic kidney disease, depression, and cardiological diseases). Recent studies show that detection of sleep apnea can be done via signal processing, especially EEG and ECG signals. However, the detection accuracy needs to be improved. In this paper, a ML model is used for the detection of sleep apnea using 19 static sensor data and 2 dynamic data (Sleep score and Arousal). The sensor data is recorded as a discrete signal and the sleep process is divided into 4.8 M segments. In this work, 19 different sensor data sets were recorded with polysomnography (PSG). These data sets have been used to perform sleep scoring. Then, arousal status marking is done. Model training was carried out with the feature vector consisting of 21 data obtained. Tests were performed with eight different machine learning techniques on a unique dataset consisting of 113 patients. After all, it was automatically determined whether people were diseased (a kind of apnea) or healthy. The proposed model had an average accuracy of 97.27%, while the recall, precision, and f-score values were 99.18%, 95.32%, and 97.20%, respectively. After all, the model that less feature engineering, less complex classification model, higher dataset usage, and higher classification performance has been revealed.
<inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameter data of analog high-speed channels or interconnects are based on Laplace transform techniques, i.e., in the ...continuous frequency domain. However, <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameter data are typically presented in tabular form. This fact does not mean that the data are coming from digital systems. The channels or interconnects are analog. Yet there is a proliferation of methods using the fast Fourier transform (FFT), which is inherently used for digital systems, applied to sampled analog <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameter data. In a previous article, we used vector fitting (VF) and bilinear transformation (BT) to place the analog <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameter data into the z-domain while developing a sampling theorem in the frequency domain (the dual of sampling in the time domain). In this article, we analyze whether using the BT, with its known frequency warping effect, has any impact on the channel impulse response when taking the inverse FFT (IFFT). In addition, the discrete Hilbert transform (DHT) is used to check for causality on the z-domain. It will be shown that by using the DHT, the <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameters can be classified as causal or not, without needing <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameter data at infinite, or data extrapolation providing that the <inline-formula> <tex-math notation="LaTeX">S </tex-math></inline-formula>-parameters complies with the sampling criterion. Examples to validate the discussed methods will be shown.
This study proposes a time-series analysis approach and a non-linear dynamics originated method to detect sub-synchronous oscillation in power systems. Mathematical expressions of the fundamental ...instantaneous signal and sample discrete signal of peak values are derived to examine the phenomenon of interaction between power system components. The results of the circulating trajectory are shown in a two-dimensional map of the calculated root-mean-square value and estimated Floquet multiplier when two signals of different modes are mixed. Without applying a digital filter or frequency decomposition, non-linear oscillation detection is possible by monitoring a non-linear oscillatory index based on the maximum Lyapunov exponent.
A standard way of describing the vocal behaviour of nonhuman primates is to classify the vocal repertoire as either graded or discrete. We analysed a large database of calls given by adult males of a ...primate considered a typical example for discrete vocal behaviour, the forest-dwelling Campbell's monkeys, Cercopithecus campbelli. We recorded vocal responses from several dozen individuals to their main predators, crowned eagles and leopards. Using cluster analysis techniques, we found two main call types, which were modified further by optional affixation of an inflexible vocal structure. It was possible to force the four call types into eight subtypes, with various degrees of gradedness. When taking context into account, we found that acoustically discrete and nonaffixed calls tended to be given right after discovering a predator, while acoustically graded and affixed calls were given during later parts of a predator encounter and to nonpredatory disturbances. In sum, our results suggest that classifications of primate vocal repertoires as either discrete or graded are likely to be meaningless, as communicatively relevant acoustic variation can be present within seemingly discrete call types.
► Primate vocal behaviour is often described as either discrete or graded. ► We experimentally studied the ostensibly discrete Campbell's monkey alarm calls. ► We found that males' alarm calls displayed both graded and discrete features. ► Alarm calls to nonurgent situations were more graded than calls to urgent situations. ► Classifying a species' calls as discrete or graded thus has little heuristic value.
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