Frequency Domain Representation Research Articles

Adaptive Subspace Tests for Multichannel Signal Detection in Auto-Regressive Disturbance

This paper deals with the problem of detecting a subspace signal in the presence of spatially and temporally colored disturbance. A new subspace parametric signal model that takes into account a multi-rank subspace structure for the target signal and employs a multi-channel auto-regressive process for the disturbance signal is proposed. Following this model, a new subspace parametric Rao detector (SP-Rao) is developed for training-limited scenarios. Unlike conventional parametric detectors that are designed for only rank-one signal detection, the SP-Rao has a new multi-rank structure with a pairwise successive spatio-temporal whitening and cross-correlation process between the observed signal and each subspace basis vector. Additionally, a non-parametric subspace detector (NSD) is derived based upon a frequency-domain representation of the SP-Rao test statistic. The NSD is distinctively different from conventional subspace detectors, in which the former involves pairwise whitening and cross-correlation between the test signal and each subspace basis vector but the latter employs the whole subspace matrix. Numerical results are presented to illustrate the performance of the proposed subspace detectors in comparison with several leading existing methods, especially in the case of limited data.

Waveform metrology: signal measurements in a modulated world

We review the waveform metrology program developed over many years at the National Institute of Standards and Technology. The goal of this program is to provide a measurement service capable of characterizing both temporal and frequency-domain instrumentation used with high-speed communication systems. Under our program, full waveforms as functions of both time and frequency are the target measurands. From these functional waveforms, traditional parametric descriptions can be derived. Furthermore, we give temporal waveforms and their frequency-domain representations consistent and equal consideration, with traceability to the International System of Units. To support this traceability, we emphasize voltage and current waveforms, their relationships, and the ability to transform both nominal values and their uncertainties from one domain to the other.

Storage in confined aquifer: Spectral analysis of groundwater in responses to Earth tides and barometric effect

AbstractDilatation of aquifer and associated water level fluctuation in groundwater well is known to be driven periodically from lunar, solar, or other tidal forces. Time‐dependent variables in groundwater system, such as water level, can be converted to power spectra in the frequency domain using Fourier transform to evaluate significant fluctuation. The major innovation of this research is to develop spectral representation in frequency domain for the groundwater system that the storage in confined aquifer can be determined considering dilatation affected by Earth tides and barometric effect. In order to verify applicability of the evolved method, time series of Earth tides and barograph are collected; aquifer storage is then determined inversely by selecting significant semidiurnal and diurnal components in spectra computation. It suggests that to discover groundwater storage using groundwater level with barograph and tidal potential of Earth in frequency domain becomes accessible and feasible.

State Feedback of Complex Systems Using Fuzzy Cognitive Maps

Complex systems have become a research area with increasing interest over the last years. The emergence of new technologies, the increase in computational power with reduced resources and cost, the integration of the physical world with computer based systems has created the possibility of significantly improving the quality of life of humans. While a significant degree of automation within these systems exists and has been provided in the past decade with examples of the smart homes and energy efficient buildings, a paradigm shift towards autonomy has been noted. The need for autonomy requires the extraction of a model; while a strict mathematical formulation usually exists for the individual subsystems, finding a complete mathematical formulation for the complex systems is a near impossible task to accomplish. For this reason, methods such as the Fuzzy Cognitive Maps (FCM) have emerged that are able to provide with a description of the complex system. The system description results from empirical observations made from experts in the related subject – integration of expert’s knowledge – that provide the required cause-effect relations between the interacting components that the FCM needs in order to be formulated. Learning methods are employed that are able to improve the formulated model based on measurements from the actual system. The FCM method, that is able to inherently integrate uncertainties, is able to provide an adequate model for the study of a complex system. With the required system model, the next step towards the development of a autonomous systems is the creation of a control scheme. While FCM can provide with a system model, the system representation proves inadequate to be utilized to design classic model based controllers that require a state space or frequency domain representation. In state space representation, the state vector contains the variables of the system that can describe enough about the system to determine its future behavior in absence of external variables. Thus, within the components – the nodes of the FCM, ideally those can be identified that constitute the state vector of the system. In this work the authors propose the creation of a state feedback control law of complex systems via Fuzzy Cognitive Maps. Given the FCM representation of a system, initially the components-states of the system are identified. Given the identified states, a FCM representation of the controller occurs where the controller parameters are the weights of the cause-effect relations of the system. The FCM of the system then is augmented with the FCM of the controller. An example of the proposed methodology is given via the use of the cart-pendulum system, a common benchmark system for testing the efficiency of control systems.

Signal Smoothing with PLS Regression.

Smoothing of instrumental signals is an important prerequisite in data processing. Various smoothing methods were suggested through the last decades each having their own benefits and drawbacks. Most of the filtering methods are based on averaging in a certain window (e.g., Savitzky-Golay) or on frequency-domain representation (e.g., Fourier filtering). The present study introduces novel approach to signal filtering based on signal variance through PLS (projections on latent structures) regression. The influence of filtering parameters on the smoothed spectrum is explained and real world examples are shown.

Multi-features taxi destination prediction with frequency domain processing.

The traditional taxi prediction methods model the taxi trajectory as a sequence of spatial points. It cannot represent two-dimensional spatial relationships between trajectory points. Therefore, many methods transform the taxi GPS trajectory into a two-dimensional image, and express the spatial correlations by trajectory image. However, the trajectory image may have noise and sparsity according to trajectory data characteristics. So, we import image frequency domain processing to taxi destination prediction to reduce noise and sparsity, then propose multi-features taxi destination prediction with frequency domain processing (MTDP-FD) method. Firstly, we transform the spatial domain trajectory image into frequency-domain representation by fast Fourier transform and reduce the noise of the trajectory images. Convolutional Neural Network (CNN) is adapted to extract the deep features from the processed trajectory image as CNN has a significant learning ability to images. Recurrent Neural Network (RNN) is adapted to predict the taxi destination as multiple hidden layers of RNN can store dependencies between input data to achieve better prediction. The deep features of the trajectory images are combined with trajectory metadata, trajectory data to act as the input to RNN. The experiments based on the taxi trajectory dataset of Porto show that the average distance error of MTDP-FD is reduced by 0.14km compared with the existing methods, and the GTOHL is the best combination of data and features to improve the prediction accuracy.

Short time Fourier transformation and deep neural networks for motor imagery brain computer interface recognition

SummaryMotor imagery (MI) is an important control paradigm in the field of brain‐computer interface (BCI), which enables the recognition of personal intention. So far, numerous methods have been designed to classify EEG signal features for MI task. However, deep neural networks have been seldom applied to analyze EEG signals. In this study, two novel kinds of deep learning schemes based on convolutional neural networks (CNN) and Long Short‐Term Memory (LSTM) were proposed for MI‐classification. The frequency domain representations of EEG signals were obtained using short time Fourier transform (STFT) to train models. Classification results were compared between conventional algorithm, CNN, and LSTM models. Compared with two other methods, CNN algorithms had shown better performance. These conclusions verified that CNN method was promising for MI‐based BCIs.

End-to-End Learning From Spectrum Data: A Deep Learning Approach for Wireless Signal Identification in Spectrum Monitoring Applications

This paper presents end-to-end learning from spectrum data-an umbrella term for new sophisticated wireless signal identification approaches in spectrum monitoring applications based on deep neural networks. End-to-end learning allows to: 1) automatically learn features directly from simple wireless signal representations, without requiring design of hand-crafted expert features like higher order cyclic moments and 2) train wireless signal classifiers in one end-to-end step which eliminates the need for complex multi-stage machine learning processing pipelines. The purpose of this paper is to present the conceptual framework of end-to-end learning for spectrum monitoring and systematically introduce a generic methodology to easily design and implement wireless signal classifiers. Furthermore, we investigate the importance of the choice of wireless data representation to various spectrum monitoring tasks. In particular, two case studies are elaborated: 1) modulation recognition and 2) wireless technology interference detection. For each case study three convolutional neural networks are evaluated for the following wireless signal representations: temporal IQ data, the amplitude/phase representation, and the frequency domain representation. From our analysis, we prove that the wireless data representation impacts the accuracy depending on the specifics and similarities of the wireless signals that need to be differentiated, with different data representations resulting in accuracy variations of up to 29%. Experimental results show that using the amplitude/phase representation for recognizing modulation formats can lead to performance improvements up to 2% and 12% for medium to high SNR compared to IQ and frequency domain data, respectively. For the task of detecting interference, frequency domain representation outperformed amplitude/phase and IQ data representation up to 20%.

High-resolution Temporal Representations of Alcohol and Tobacco Behaviors from Social Media Data.

Understanding tobacco- and alcohol-related behavioral patterns is critical for uncovering risk factors and potentially designing targeted social computing intervention systems. Given that we make choices multiple times per day, hourly and daily patterns are critical for better understanding behaviors. Here, we combine natural language processing, machine learning and time series analyses to assess Twitter activity specifically related to alcohol and tobacco consumption and their sub-daily, daily and weekly cycles. Twitter self-reports of alcohol and tobacco use are compared to other data streams available at similar temporal resolution. We assess if discussion of drinking by inferred underage versus legal age people or discussion of use of different types of tobacco products can be differentiated using these temporal patterns. We find that time and frequency domain representations of behaviors on social media can provide meaningful and unique insights, and we discuss the types of behaviors for which the approach may be most useful.

Dynamic Modelling and Control of a Reciprocating Engine

Nowadays energy systems should be considered as integrated energy systems (IESs), where interactions between different energy vectors affect each other. A good performance of the whole system depends on the adequate behaviour of each individual element as undesired dynamics may propagate from one element to another. Due to the system complexity, a common practice is to employ steady-state models. Although such an approach is valuable as it provides significant insight into the system behaviour, it may hide inherent coupling characteristics as the dynamics are not considered. To ensure the satisfactory performance of each component, dynamic models are not only required, but essential. With a truly dynamic model it is possible to clearly understand how the system is affected by different operating conditions, load variations and disturbances over time, which in turn enables an effective control system design. Following this line, this paper presents a mathematical model, based on the mean value approach, of a reciprocating engine, which is used in combined heat and power units – key component of an IES. Although the system is non-linear, it is shown that a single-input single-output linear system can be derived and, thus, a frequency domain representation suitable for control system design can be obtained. The system has been developed in MATLAB/Simulink. Simulation results show that the designed linear controller is capable of ensuring a good performance of the reciprocating engine non-linear model.

EEG Frequency-Tagging and Input-Output Comparison in Rhythm Perception.

The combination of frequency-tagging with electroencephalography (EEG) has recently proved fruitful for understanding the perception of beat and meter in musical rhythm, a common behavior shared by humans of all cultures. EEG frequency-tagging allows the objective measurement of input-output transforms to investigate beat perception, its modulation by exogenous and endogenous factors, development, and neural basis. Recent doubt has been raised about the validity of comparing frequency-domain representations of auditory rhythmic stimuli and corresponding EEG responses, assuming that it implies a one-to-one mapping between the envelope of the rhythmic input and the neural output, and that it neglects the sensitivity of frequency-domain representations to acoustic features making up the rhythms. Here we argue that these elements actually reinforce the strengths of the approach. The obvious fact that acoustic features influence the frequency spectrum of the sound envelope precisely justifies taking into consideration the sounds used to generate a beat percept for interpreting neural responses to auditory rhythms. Most importantly, the many-to-one relationship between rhythmic input and perceived beat actually validates an approach that objectively measures the input-output transforms underlying the perceptual categorization of rhythmic inputs. Hence, provided that a number of potential pitfalls and fallacies are avoided, EEG frequency-tagging to study input-output relationships appears valuable for understanding rhythm perception.

Acoustics of snoring and automatic snore sound detection in children

Objective: Acoustic analyses of snoring sounds have been used to objectively assess snoring and applied in various clinical problems for adult patients. Such studies require highly automatized tools to analyze the sound recordings of the whole night’s sleep, in order to extract clinically relevant snore- related statistics. The existing techniques and software used for adults are not efficiently applicable to snoring sounds in children, basically because of different acoustic signal properties. In this paper, we present a broad range of acoustic characteristics of snoring sounds in children (N = 38) in comparison to adult (N = 30) patients. Approach: Acoustic characteristics of the signals were calculated, including frequency domain representations, spectrogram-based characteristics, spectral envelope analysis, formant structures and loudness of the snoring sounds. Main results: We observed significant differences in spectral features, formant structures and loudness of the snoring signals of children compared to adults that may arise from the diversity of the upper airway anatomy as the principal determinant of the snore sound generation mechanism. Furthermore, based on the specific audio features of snoring children, we proposed a novel algorithm for the automatic detection of snoring sounds from ambient acoustic data specifically in a pediatric population. The respiratory sounds were recorded using a pair of microphones and a multi-channel data acquisition system simultaneously with full-night polysomnography during sleep. Brief sound chunks of 0.5 s were classified as either belonging to a snoring event or not with a multi-layer perceptron, which was trained in a supervised fashion using stochastic gradient descent on a large hand-labeled dataset using frequency domain features. Significance: The method proposed here has been used to extract snore-related statistics that can be calculated from the detected snore episodes for the whole night’s sleep, including number of snore episodes (total snoring time), ratio of snore to whole sleep time, variation of snoring rate, regularity of snoring episodes in time and amplitude and snore loudness. These statistics will ultimately serve as a clinical tool providing information for the objective evaluation of snoring for several clinical applications.

On Space-Time Filtering Framework for Matching Human Actions Across Different Viewpoints.

Space-time template matching is considered as a promising approach for human action recognition. However, a major drawback of template-based methods is computational overhead due to matching in spatial domain. Recently, space-time correlation-based action filters have been proposed for recognizing human actions in frequency domain. These action filters present reduction in time complexity as Fourier transform-based matching is faster than spatial template matching. However, the utility of such action filters is challenged due to a number of factors: 1) inability to deal with view variations due to implicit lack of support for view-invariance; 2) these filters can be trained only for one action class at a time, and separate filters are required for each action class with increased computational overhead; 3) these filters simply take average of similar action instances and behave no better than average filters; and 4) slightly misaligned action data sets create problems as these filters are not shift-invariant. In this paper, we try to address these shortcomings by proposing an advanced space-time filtering framework for recognizing human actions despite large viewpoint variations. Rather than using crude intensity values, we use 3D tensor structure at each pixel, which characterizes the most common local motion in action sequences. Discrete tensor Fourier transform is then applied to achieve frequency domain representations. Then, we form view clusters from multiple view action data and use space-time correlation filtering to achieve discriminative view representations. These representations are used in an innovative way to achieve action recognition despite viewpoint variations. Extensive experimentation is performed on well-known multiple view action data sets, including IXMAS, WVU, and N-UCLA action data set. A detailed performance comparison with the existing view-invariant action recognition techniques indicates that our approach works equally well for RGB and RGB-D video data with increased accuracy and efficiency.

Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.

FRF-based structural parameters estimation using strain data: sensitivity equation, measurement and excitation selection

In this paper, a structural model updating technique is presented using frequency domain representation of incomplete strain data to identify the location and severity of structural damages. The most important challenges of model updating methods such as selection of excitation, measurement locations and interested frequency ranges are addressed. Distribution of strain energy in all structural elements and norms of the derived sensitivity equation are utilized for the selection of measurement and excitation locations. The important effect of different level of noise in measurement data and modelling error on the accuracy and robustness of the proposed method are investigated. A bowstring truss and a two-storey single-bay frame are used to evaluate the numerical ability of proposed method. The results prove the potentials of the proposed method in identifying the location and severity of damage in the presence of different errors.

Design Of Area Efficient R2MDC FFT Using Optimized Complex Multiplier

Fast Fourier Transformation (FFT) algorithm is the frequency transformation technique in which time domain representation of sampled signal is converted into frequency domain representation of sampled one. In this paper, low complexity Radix-2 Multi-path Delay Commutator (R2MDC) FFT frequency transformation technique is developed through Very Large Scale Integration (VLSI) System design environment. Low power consumption, less area and low delay are the main concerns in VLSI. Traditional Radix-2 MDC FFT structure has more hardware complexity due to its intensive computational elements. In general, complex multiplier structure of R2MDC FFT requires more LUTs and slices than other structure. In order to overcome this problem, complex multiplier architecture of R2MDC FFT is effectively optimized in this paper. Proposed optimized complex multiplier architecture consumes less hardware complexity than existing one. Further, design of R2MDC FFT architecture by using optimized complexity multiplier offer more advantages. Simulation results for proposed low complexity R2MDC FFT architecture is evaluated by using Model-Sim6.3C and synthesis results are evaluated by using Xilinx 10.1 design tool.

Binaural Sound Localization Based on Reverberation Weighting and Generalized Parametric Mapping

Binaural sound source localization is an important technique for speech enhancement, video conferencing, and human-robot interaction, etc. However, in realistic scenarios, the reverberation and environmental noise would degrade the precision of sound direction estimation. Therefore, reliable sound localization is essential to practical applications. To deal with these disturbances, this paper presents a novel binaural sound source localization approach based on reverberation weighting and generalized parametric mapping. First, the reverberation weighting as a preprocessing stage, is used to separately suppress the early and late reverberation, while preserving interaural cues. Then, two binaural cues, i.e., interaural time and intensity differences, are extracted from the frequency-domain representations of dereverberated binaural signals for the online localization. Their corresponding templates are established using the training data. Furthermore, the generalized parametric mapping is proposed to build a generalized parametric model for describing relationships between azimuth and binaural cues analytically. Finally, a two-step sound localization process is introduced to refine azimuth estimation based on the generalized parametric model and template matching. Experiments in both simulated and real scenarios validate that the proposed method can achieve better localization performance compared to state-of-the-art methods.

FFT Consolidated Sparse and Collaborative Representation for Image Classification

Spectrum analysis can quickly extract and analyze frequency domain features of signal, and it has been widely applied in fields of image processing, noise processing and signal processing. Fast Fourier transform (FFT) is fast and efficient, because it can efficiently decrease complexity of discrete Fourier transform. As a consequence, FFT is a very good method for image frequency spectrum analysis. In this paper, we propose to consolidate frequency domain representation by sparse representation (SR) and collaborative representation classification (CRC) which has excellent performance in comparison with general sparse representation-associated classification algorithms. Our proposed novel method has three main phases. The first phase utilizes FFT to extract frequency domain features of original images, which are complementary with representations of the original images. The second phase of our proposed novel method exploits CRC or SR to obtain scores of original images and obtained features, respectively. The third phase integrates the scores of original images and obtained features and uses them to classify images. The major contribution of the proposed method is that it is usually more robust than methods using only FFT, CRC or state-of-art method CIRLRC for image classification. The experiments of image classification demonstrate that the simultaneous use of FFT and CRC or sparse representation classification has high accuracy on image recognition.

Analytical Derivation of Nonlinear Spectral Effects and 1/f Scaling Artifact in Signal Processing of Real-World Data.

In estimating the frequency spectrum of real-world time series data, we must violate the assumption of infinite-length, orthogonal components in the Fourier basis. While it is widely known that care must be taken with discretely sampled data to avoid aliasing of high frequencies, less attention is given to the influence of low frequencies with period below the sampling time window. Here, we derive an analytic expression for the side-lobe attenuation of signal components in the frequency domain representation. This expression allows us to detail the influence of individual frequency components throughout the spectrum. The first consequence is that the presence of low-frequency components introduces a 1/f[Formula: see text] component across the power spectrum, with a scaling exponent of [Formula: see text]. This scaling artifact could be composed of diffuse low-frequency components, which can render it difficult to detect a priori. Further, treatment of the signal with standard digital signal processing techniques cannot easily remove this scaling component. While several theoretical models have been introduced to explain the ubiquitous 1/f[Formula: see text] scaling component in neuroscientific data, we conjecture here that some experimental observations could be the result of such data analysis procedures.

Restoration of missing data in limited angle tomography based on Helgason–Ludwig consistency conditions

In limited angle tomography, missing data in an insufficient angular scan will cause streak artifacts in the reconstructed images. Correspondingly, in the frequency domain representation of the imaged object, a double wedge-shaped region is missing. In this paper, we perform a regression in sinogram domain and an image fusion in frequency domain to restore the missing data. We first convert the sinogram restoration problem into a regression problem based on the Helgason–Ludwig consistency conditions. Due to its severe ill-posedness, regression only partially recovers the correct frequency components, especially lower frequency components, and will introduce erroneous ones, particularly higher frequencies. Bilateral filtering is utilized to retain the most prominent high frequency components and suppress erroneous ones. Afterwards, a fusion in the frequency domain utilizes the restored frequency components to fill the missing double wedge region. The proposed method is evaluated in a parallel-beam study on both numerical and clinical phantoms. The root-mean-square errors of the reconstructed images decrease from 302 to 78 HU for the noise-free Shepp–Logan phantom, from 355 to 175 HU for the noisy Shepp–Logan phantom, and from 187 to 56 HU for the clinical data. The results show that our method is promising in streak reduction and intensity offset compensation in both noise-free and noisy situations.