25,051 research outputs found

    IF Estimation for Multicomponent Signals Using Image Processing Techniques in the Time-Frequency Domain

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    This paper presents a method for estimating the instantaneous frequency (IF) of multicomponent signals. The technique involves, firstly, the transformation of the one dimensional signal to the two dimensional time-frequency domain using a reduced interference quadratic time-frequency distribution. IF estimation of signal components is then achieved by implementing two image processing steps: local peak detection of the time--frequency (TF) representation followed by an image processing technique called component linking. The proposed IF estimator is tested on noisy synthetic monocomponent and multicomponent signals exhibiting linear and nonlinear laws. For low signal to noise ratio (SNR) environments, a time-frequency peak filtering preprocessing step is used for signal enhancement. Application of the IF estimation scheme to real signals is illustrated with newborn EEG signals. Finally, to illustrate the potential use of the proposed IF estimation method in classifying signals based on their TF components' IFs, a classification method using least squares data-fitting is proposed and illustrated on synthetic and real signals

    The Statistical Performance of Some Instantaneous Frequency Estimators

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    We examine the class of smoothed central finite differences (SCFD) instantaneous frequency (IF) estimators which are based on finite differencing of the phase of the analytic signal. These estimators are of particular interest since they are closely related to IF estimation via (periodic) first moment , with respect to frequency, of discrete time frequency representations (TFRs) in Cohen's class (TFR moment IF estimators). Cohen's class includes representation such as the spectrogram and Wigner-Ville distribution. Indeed in the case of a monocomponent signal, the variance of a TFR moment IF estimator is bound from below by the variance of the corresponding SCFD estimator. We determine the distribution of these class of estimators and establish a framework which allows the comparison of several other estimators such as the zero crossing estimator and a recently proposed estimator based on linear regression on the signal phase. We can find the regression IF estimator is biased and exhibits a large threshold for much of the frequency range because it does not account for the circular nature of discrete time frequency estimates. By replacing the linear convolution operation on the regression estimator with the appropriate convolution operation for circular data we obtain the parabolic SCFD (PSCFD) estimator. This estimator is unbiased and has a frequency independent variance and yet still remains the optimal performance and simplicity of the original estimator. The PSCFD estimator would be suitable for use as a real-time line or bearing tracker. In this paper, we propose a number of mathematical operations suitable for circular data which should be used in preference to the conventional linear operations

    A modulation property of time-frequency derivatives of filtered phase and its application to aperiodicity and fo estimation

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    We introduce a simple and linear SNR (strictly speaking, periodic to random power ratio) estimator (0dB to 80dB without additional calibration/linearization) for providing reliable descriptions of aperiodicity in speech corpus. The main idea of this method is to estimate the background random noise level without directly extracting the background noise. The proposed method is applicable to a wide variety of time windowing functions with very low sidelobe levels. The estimate combines the frequency derivative and the time-frequency derivative of the mapping from filter center frequency to the output instantaneous frequency. This procedure can replace the periodicity detection and aperiodicity estimation subsystems of recently introduced open source vocoder, YANG vocoder. Source code of MATLAB implementation of this method will also be open sourced.Comment: 8 pages 9 figures, Submitted and accepted in Interspeech201

    SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

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    A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm

    A Fourier transform method for nonparametric estimation of multivariate volatility

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    We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Multi-Level Pre-Correlation RFI Flagging for Real-Time Implementation on UniBoard

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    Because of the denser active use of the spectrum, and because of radio telescopes higher sensitivity, radio frequency interference (RFI) mitigation has become a sensitive topic for current and future radio telescope designs. Even if quite sophisticated approaches have been proposed in the recent years, the majority of RFI mitigation operational procedures are based on post-correlation corrupted data flagging. Moreover, given the huge amount of data delivered by current and next generation radio telescopes, all these RFI detection procedures have to be at least automatic and, if possible, real-time. In this paper, the implementation of a real-time pre-correlation RFI detection and flagging procedure into generic high-performance computing platforms based on Field Programmable Gate Arrays (FPGA) is described, simulated and tested. One of these boards, UniBoard, developed under a Joint Research Activity in the RadioNet FP7 European programme is based on eight FPGAs interconnected by a high speed transceiver mesh. It provides up to ~4 TMACs with Altera Stratix IV FPGA and 160 Gbps data rate for the input data stream. Considering the high in-out data rate in the pre-correlation stages, only real-time and go-through detectors (i.e. no iterative processing) can be implemented. In this paper, a real-time and adaptive detection scheme is described. An ongoing case study has been set up with the Electronic Multi-Beam Radio Astronomy Concept (EMBRACE) radio telescope facility at Nan\c{c}ay Observatory. The objective is to evaluate the performances of this concept in term of hardware complexity, detection efficiency and additional RFI metadata rate cost. The UniBoard implementation scheme is described.Comment: 16 pages, 13 figure
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