812 research outputs found

    Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis

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    The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose the novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal (FSAS) representations with following properties: (1) real part of eight FSAS representations is the original signal and imaginary part is the FCQT of the real part, (2) imaginary part of eight FSAS representations is the original signal and real part is the FSQT of the real part, (3) like the GAS, Fourier spectrum of the all FSAS representations has only positive frequencies, however unlike the GAS, the real and imaginary parts of the proposed FSAS representations are not orthogonal to each other. The Fourier decomposition method (FDM) is an adaptive data analysis approach to decompose a signal into a set of small number of Fourier intrinsic band functions which are AM-FM components. This study also proposes a new formulation of the FDM using the discrete cosine transform (DCT) with the GAS and FSAS representations, and demonstrate its efficacy for improved time-frequency-energy representation and analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure

    Assessment of vocal cord nodules: A case study in speech processing by using Hilbert-Huang Transform

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    Vocal cord nodules represent a pathological condition for which the growth of unnatural masses on vocal folds affects the patients. Among other effects, changes in the vocal cords' overall mass and stiffness alter their vibratory behaviour, thus changing the vocal emission generated by them. This causes dysphonia, i.e. abnormalities in the patients' voice, which can be analysed and inspected via audio signals. However, the evaluation of voice condition through speech processing is not a trivial task, as standard methods based on the Fourier Transform, fail to fit the non-stationary nature of vocal signals. In this study, four audio tracks, provided by a volunteer patient, whose vocal fold nodules have been surgically removed, were analysed using a relatively new technique: the Hilbert-Huang Transform (HHT) via Empirical Mode Decomposition (EMD); specifically, by using the CEEMDAN (Complete Ensemble EMD with Adaptive Noise) algorithm. This method has been applied here to speech signals, which were recorded before removal surgery and during convalescence, to investigate specific trends. Possibilities offered by the HHT are exposed, but also some limitations of decomposing the signals into so-called intrinsic mode functions (IMFs) are highlighted. The results of these preliminary studies are intended to be a basis for the development of new viable alternatives to the softwares currently used for the analysis and evaluation of pathological voice

    On the mechanism of response latencies in auditory nerve fibers

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    Despite the structural differences of the middle and inner ears, the latency pattern in auditory nerve fibers to an identical sound has been found similar across numerous species. Studies have shown the similarity in remarkable species with distinct cochleae or even without a basilar membrane. This stimulus-, neuron-, and species- independent similarity of latency cannot be simply explained by the concept of cochlear traveling waves that is generally accepted as the main cause of the neural latency pattern. An original concept of Fourier pattern is defined, intended to characterize a feature of temporal processing—specifically phase encoding—that is not readily apparent in more conventional analyses. The pattern is created by marking the first amplitude maximum for each sinusoid component of the stimulus, to encode phase information. The hypothesis is that the hearing organ serves as a running analyzer whose output reflects synchronization of auditory neural activity consistent with the Fourier pattern. A combined research of experimental, correlational and meta-analysis approaches is used to test the hypothesis. Manipulations included phase encoding and stimuli to test their effects on the predicted latency pattern. Animal studies in the literature using the same stimulus were then compared to determine the degree of relationship. The results show that each marking accounts for a large percentage of a corresponding peak latency in the peristimulus-time histogram. For each of the stimuli considered, the latency predicted by the Fourier pattern is highly correlated with the observed latency in the auditory nerve fiber of representative species. The results suggest that the hearing organ analyzes not only amplitude spectrum but also phase information in Fourier analysis, to distribute the specific spikes among auditory nerve fibers and within a single unit. This phase-encoding mechanism in Fourier analysis is proposed to be the common mechanism that, in the face of species differences in peripheral auditory hardware, accounts for the considerable similarities across species in their latency-by-frequency functions, in turn assuring optimal phase encoding across species. Also, the mechanism has the potential to improve phase encoding of cochlear implants

    Low-cost device for fault diagnosis in bearings based on the Hilbert-Huang transform

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    In order to monitor the condition of machinery complex industrial environments, high-cost equipment is required for signal acquisition and processing. However, low-cost sensor nodes with high processing capability are a potential solution to improve diagnostic systems. This paper presents a low-cost device for fault diagnosis based on the vibration response in rotating machines with the implementation of the Hilbert-Huang transform (HHT) analysis to extract the main characteristics of the signal. HHT, used to analyze non-linear and non-stationary signals, incorporates an Empirical Mode Decomposition (EMD) process. Processing is carried out in an embedded system to acquire vibration response data and extract signal characteristics that allow condition monitoring. As a result of local processing in the vibratory measurement device in an embedded system, the signal decomposition is performed, enabling the detection of the characteristic failure in the bearing ring and transmitting the alarm to a hub. This eliminates the need for a central diagnostic system and reduces the total cost of the system.This work has been carried out within the framework of the Looming Factory project, reference 001-P-001643, of the RIS3CAT program of the Generalitat de Catalunya. This research has been made possible thanks to the support of the MCIA Electronic Drives and Industrial Applications Research Group of the Universitat Politècnica de Catalunya and its collaborators.Peer ReviewedPostprint (published version

    Pitch Estimation of Stereophonic Mixtures of Delay and Amplitude Panned Signals

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    Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese

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    Mandarin Chinese is characterized by being a tonal language; the pitch (or F0F_0) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in amplitude and phase which must be accounted for in any analysis which attempts to provide a linguistically meaningful description of the language. A joint model for amplitude, phase and duration is presented which combines elements from Functional Data Analysis, Compositional Data Analysis and Linear Mixed Effects Models. By decomposing functions via a functional principal component analysis, and connecting registration functions to compositional data analysis, a joint multivariate mixed effect model can be formulated which gives insights into the relationship between the different modes of variation as well as their dependence on linguistic and non-linguistic covariates. The model is applied to the COSPRO-1 data set, a comprehensive database of spoken Taiwanese Mandarin, containing approximately 50 thousand phonetically diverse sample F0F_0 contours (syllables), and reveals that phonetic information is jointly carried by both amplitude and phase variation.Comment: 49 pages, 13 figures, small changes to discussio
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