Analyse des signaux AM-FM basée sur une version B-splines de l'EMD-ESA

In this paper a signal analysis framework for estimating time-varying amplitude and frequency functions of multicomponent amplitude and frequency modulated (AM–FM) signals is introduced. This framework is based on local and non-linear approaches, namely Energy Separation Algorithm (ESA) and Empirical Mode Decomposition (EMD). Conjunction of Discrete ESA (DESA) and EMD is called EMD–DESA. A new modified version of EMD where smoothing instead of an interpolation to construct the upper and lower envelopes of the signal is introduced. Since extracted IMFs are represented in terms of B-spline (BS) expansions, a closed formula of ESA robust against noise is used. Instantaneous Frequency (IF) and Instantaneous Amplitude (IA) estimates of a multi- component AM–FM signal, corrupted with additive white Gaussian noise of varying SNRs, are analyzed and results compared to ESA, DESA and Hilbert transform-based algorithms. SNR and MSE are used as figures of merit. Regularized BS version of EMD– ESA performs reasonably better in separating IA and IF components compared to the other methods from low to high SNR. Overall, obtained results illustrate the effective- ness of the proposed approach in terms of accuracy and robustness against noise to track IF and IA features of a multicomponent AM–FM signal

AM-FM methods for image and video processing

This dissertation is focused on the development of robust and efficient Amplitude-Modulation Frequency-Modulation (AM-FM) demodulation methods for image and video processing (there is currently a patent pending that covers the AM-FM methods and applications described in this dissertation). The motivation for this research lies in the wide number of image and video processing applications that can significantly benefit from this research. A number of potential applications are developed in the dissertation. First, a new, robust and efficient formulation for the instantaneous frequency (IF) estimation: a variable spacing, local quadratic phase method (VS-LQP) is presented. VS-LQP produces much more accurate results than current AM-FM methods. At significant noise levels (SNR \u3c 30dB), for single component images, the VS-LQP method produces better IF estimation results than methods using a multi-scale filterbank. At low noise levels (SNR \u3e 50dB), VS-LQP performs better when used in combination with a multi-scale filterbank. In all cases, VS-LQP outperforms the Quasi-Eigen Approximation algorithm by significant amounts (up to 20dB). New least squares reconstructions using AM-FM components from the input signal (image or video) are also presented. Three different reconstruction approaches are developed: (i) using AM-FM harmonics, (ii) using AM-FM components extracted from different scales and (iii) using AM-FM harmonics with the output of a low-pass filter. The image reconstruction methods provide perceptually lossless results with image quality index values bigger than 0.7 on average. The video reconstructions produced image quality index values, frame by frame, up to more than 0.7 using AM-FM components extracted from different scales. An application of the AM-FM method to retinal image analysis is also shown. This approach uses the instantaneous frequency magnitude and the instantaneous amplitude (IA) information to provide image features. The new AM-FM approach produced ROC area of 0.984 in classifying Risk 0 versus Risk 1, 0.95 in classifying Risk 0 versus Risk 2, 0.973 in classifying Risk 0 versus Risk 3 and 0.95 in classifying Risk 0 versus all images with any sign of Diabetic Retinopathy. An extension of the 2D AM-FM demodulation methods to three dimensions is also presented. New AM-FM methods for motion estimation are developed. The new motion estimation method provides three motion estimation equations per channel filter (AM, IF motion equations and a continuity equation). Applications of the method in motion tracking, trajectory estimation and for continuous-scale video searching are demonstrated. For each application, we discuss the advantages of the AM-FM methods over current approaches

Embedded AM-FM Signal Decomposition Algorithm for Continuous Human Activity Monitoring

AM-FM decomposition techniques have been successfully used for extracting significative features from a large variety of signals, helping realtime signal monitoring and pattern recognition, since they represent signals as a simultaneous composition of amplitude modulation and frequency modulation, where the carriers, amplitude envelopes, and the instantaneous frequencies are the features to be estimated. Human activities often involve repetitive movements, such as in running or cycling, where sinusoidal AM-FM decompositions of signals have already demonstrated to be useful to extract compact features to aid monitoring, classification, or detection. In this work we thus present the challenges and results of implementing the iterated coherent Hilbert decomposition (ICHD), a particularly effective algorithm to obtain an AM-FM decomposition, within a resource-constrained and low-power ARM Cortex-M4 microcontroller that is present in a wearable sensor we developed. We apply ICHD to the gyroscope data acquired from an inertial measurement unit (IMU) that is present in the sensor. Optimizing the implementation allowed us to achieve real-time performance using less then 16 % of the available CPU time, while consuming only about 5.4 mW of power, which results in a run-time of over 7 days using a small 250 mAh rechargeable cell

Some Advances in Nonlinear Speech Modeling Using Modulations, Fractals, and Chaos

In this paper we briefly summarize our on-going work on modeling nonlinear structures in speech signals, caused by modulation and turbulence phenomena, using the theories of modulation, fractals, and chaos as well as suitable nonlinear signal analysis methods. Further, we focus on two advances: i) AM-FM modeling of fricative sounds with random modulation signals of the 1/f-noise type and ii) improved methods for speech analysis and prediction on reconstructed multidimensional attractors. 1

Une nouvelle classe d'opérateurs de Teager-Kaiser multidimensionnels basée sur les dérivées directionnelles d'ordre supérieur

This work aims at introducing some energy operators linked to Teager-Kaiser energy operator and its associated higher order versions and expand them to multidimensional signals. These operators are very useful for analyzing oscillatory signals with time-varying amplitude and frequency (AM-FM). We prove that gradient tensors combined with Kronecker powers allow to express these operators by directional derivatives along any n-D vector. In particular, we show that the construction of a large class of non linear operators for AM-FM multidimensional signal demodulation is possible. Also, a new scalar function using the directional derivative along a vector giving the ”sign” of the frequency components is introduced. An application of this model to local n-D AM-FM signal is presented and related demodulation error rates estimates. To show the effectiveness and the robustness of our method in term of envelope and frequency components extraction, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm and to our recently introduced n-D operator

Statistical models for natural sounds

It is important to understand the rich structure of natural sounds in order to solve important tasks, like automatic speech recognition, and to understand auditory processing in the brain. This thesis takes a step in this direction by characterising the statistics of simple natural sounds. We focus on the statistics because perception often appears to depend on them, rather than on the raw waveform. For example the perception of auditory textures, like running water, wind, fire and rain, depends on summary-statistics, like the rate of falling rain droplets, rather than on the exact details of the physical source. In order to analyse the statistics of sounds accurately it is necessary to improve a number of traditional signal processing methods, including those for amplitude demodulation, time-frequency analysis, and sub-band demodulation. These estimation tasks are ill-posed and therefore it is natural to treat them as Bayesian inference problems. The new probabilistic versions of these methods have several advantages. For example, they perform more accurately on natural signals and are more robust to noise, they can also fill-in missing sections of data, and provide error-bars. Furthermore, free-parameters can be learned from the signal. Using these new algorithms we demonstrate that the energy, sparsity, modulation depth and modulation time-scale in each sub-band of a signal are critical statistics, together with the dependencies between the sub-band modulators. In order to validate this claim, a model containing co-modulated coloured noise carriers is shown to be capable of generating a range of realistic sounding auditory textures. Finally, we explored the connection between the statistics of natural sounds and perception. We demonstrate that inference in the model for auditory textures qualitatively replicates the primitive grouping rules that listeners use to understand simple acoustic scenes. This suggests that the auditory system is optimised for the statistics of natural sounds