A time-frequency based method for the detection and tracking of multiple non-linearly modulated components with births and deaths

International audienceThe estimation of the components which contain the characteristics of a signal attracts great attention in many real world applications. In this paper, we address the problem of the tracking of multiple signal components over discrete time series. We propose an algorithm to first detect the components from a given time-frequency distribution and then to track them automatically. In the first place, the peaks corresponding to the signal components are detected using the statistical properties of the spectral estimator. Then, an original classifier is proposed to automatically track the detected peaks in order to build components over time. This classifier is based on a total divergence matrix computed from a peak-component divergence matrix that takes account of both amplitude and frequency information. The peak-component pairs are matched automatically from this divergence matrix. We propose a stochastic discrimination rule to decide upon the acceptance of the peak-component pairs. In this way, the algorithm can estimate the number, the amplitude and frequency modulation functions, and the births and the deaths of the components without any limitation on the number of components. The performance of the proposed method, a post-processing of a time-frequency distribution is validated on simulated signals under different parameter sets. The method is also applied to 4 real-world signals as a proof of its applicability. Index Terms—Time-frequency domain, multicomponent, peak detection, component tracking, amplitude and frequency modulation , nonlinear, nonstationary, births and death

Modeling and frequency tracking of marine mammal whistle calls

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2009Marine mammal whistle calls present an attractive medium for covert underwater communications. High quality models of the whistle calls are needed in order to synthesize natural-sounding whistles with embedded information. Since the whistle calls are composed of frequency modulated harmonic tones, they are best modeled as a weighted superposition of harmonically related sinusoids. Previous research with bottlenose dolphin whistle calls has produced synthetic whistles that sound too “clean” for use in a covert communications system. Due to the sensitivity of the human auditory system, watermarking schemes that slightly modify the fundamental frequency contour have good potential for producing natural-sounding whistles embedded with retrievable watermarks. Structured total least squares is used with linear prediction analysis to track the time-varying fundamental frequency and harmonic amplitude contours throughout a whistle call. Simulation and experimental results demonstrate the capability to accurately model bottlenose dolphin whistle calls and retrieve embedded information from watermarked synthetic whistle calls. Different fundamental frequency watermarking schemes are proposed based on their ability to produce natural sounding synthetic whistles and yield suitable watermark detection and retrieval

Studies of relativistic backward-wave oscillator operation in the cross-excitation regime

We first reported the operation of a relativistic backward-wave oscillator (BWO) in the so-called cross-excitation regime in 1998. This instability, whose general properties were predicted earlier through numerical studies, resulted from the use of a particularly shallow rippled-wall waveguide [slow wave structure (SWS)] that was installed in an experiment to diagnose pulse shortening in a long-pulse electron beam-driven high-power microwave (HPM) source. This SWS was necessary to accommodate laser interferometry measurements along the SWS during the course of microwave generation. Since those early experiments, we have studied this regime in greater detail using two different SWS lengths. We have invoked time-frequency analysis, the smoothed-pseudo Wigner-Ville distribution in particular, to interpret the heterodyned signals of the radiated power measurements. These recent results are consistent with earlier theoretical predictions for the onset and voltage scaling for this instability. This paper presents data for a relativistic BWO operating in the single-frequency regime for two axial modes, operating in the cross-excitation regime, and discusses the interpretation of the data, as well as the methodology used for its analysis. Although operation in the cross-excitation regime is typically avoided due to its poorer efficiency, it may prove useful for future HPM effects studies

A tutorial review on time-frequency analysis of non-stationary vibration signals with nonlinear dynamics applications

Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equation

Tracking Rhythmicity in Biomedical Signals using Sequential Monte Carlo methods

Cyclical patterns are common in signals that originate from natural systems such as the human body and man-made machinery. Often these cyclical patterns are not perfectly periodic. In that case, the signals are called pseudo-periodic or quasi-periodic and can be modeled as a sum of time-varying sinusoids, whose frequencies, phases, and amplitudes change slowly over time. Each time-varying sinusoid represents an individual rhythmical component, called a partial, that can be characterized by three parameters: frequency, phase, and amplitude. Quasi-periodic signals often contain multiple partials that are harmonically related. In that case, the frequencies of other partials become exact integer multiples of that of the slowest partial. These signals are referred to as multi-harmonic signals. Examples of such signals are electrocardiogram (ECG), arterial blood pressure (ABP), and human voice. A Markov process is a mathematical model for a random system whose future and past states are independent conditional on the present state. Multi-harmonic signals can be modeled as a stochastic process with the Markov property. The Markovian representation of multi-harmonic signals enables us to use state-space tracking methods to continuously estimate the frequencies, phases, and amplitudes of the partials. Several research groups have proposed various signal analysis methods such as hidden Markov Models (HMM), short time Fourier transform (STFT), and Wigner-Ville distribution to solve this problem. Recently, a few groups of researchers have proposed Monte Carlo methods which estimate the posterior distribution of the fundamental frequency in multi-harmonic signals sequentially. However, multi-harmonic tracking is more challenging than single-frequency tracking, though the reason for this has not been well understood. The main objectives of this dissertation are to elucidate the fundamental obstacles to multi-harmonic tracking and to develop a reliable multi-harmonic tracker that can track cyclical patterns in multi-harmonic signals

Modulation vocoder for analysis, processing and synthesis of audio signals with application to frequency selective pitch transposition

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Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Combined-channel instantaneous frequency analysis for audio source separation based on comodulation

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2008.Includes bibliographical references (p. 295-303).Normal human listeners have a remarkable ability to focus on a single sound or speaker of interest and to block out competing sound sources. Individuals with hearing impairments, on the other hand, often experience great difficulty in noisy environments. The goal of our research is to develop novel signal processing methods inspired by neural auditory processing that can improve current speech separation systems. These could potentially be of use as assistive devices for the hearing impaired, and in many other communications applications. Our focus is the monaural case where spatial information is not available. Much perceptual evidence indicates that detecting common amplitude and frequency variation in acoustic signals plays an important role in the separation process. The physical mechanisms of sound generation in many sources cause common onsets/offsets and correlated increases/decreases in both amplitude and frequency among the spectral components of an individual source, which can potentially serve as a distinct signature. However, harnessing these common modulation patterns is difficult because when spectral components of competing sources overlap within the bandwidth of a single auditory filter, the modulation envelope of the resultant waveform resembles that of neither source. To overcome this, for the coherent, constant-frequency AM case, we derive a set of matrix equations which describes the mixture, and we prove that there exists a unique factorization under certain constraints. These constraints provide insight into the importance of onset cues in source separation. We develop algorithms for solving the system in those cases in which a unique solution exists. This work has direct bearing on the general theory of non-negative matrix factorization which has recently been applied to various problems in biology and learning. For the general, incoherent, AM and FM case, the situation is far more complex because constructive and destructive interference between sources causes amplitude fluctuations within channels that obscures the modulation patterns of individual sources.(cont.) Motivated by the importance of temporal processing in the auditory system, and specifically, the use of extrema, we explore novel methods for estimating instantaneous amplitude, frequency, and phase of mixtures of sinusoids by comparing the location of local maxima of waveforms from various frequency channels. By using an overlapping exponential filter bank model with properties resembling the cochlea, and combining information from multiple frequency bands, we are able to achieve extremely high frequency and time resolution. This allows us to isolate and track the behavior of individual spectral components which can be compared and grouped with others of like type. Our work includes both computational and analytic approaches to the general problem. Two suites of tests were performed. The first were comparative evaluations of three filter-bank-based algorithms on sets of harmonic-like signals with constant frequencies. One of these algorithms was selected for further performance tests on more complex waveforms, including AM and FM signals of various types, harmonic sets in noise, and actual recordings of male and female speakers, both individual and mixed. For the frequency-varying case, initial results of signal analysis with our methods appear to resolve individual sidebands of single harmonics on short time scales, and raise interesting conceptual questions on how to define, use and interpret the concept of instantaneous frequency. Based on our results, we revisit a number of questions in current auditory research, including the need for both rate and place coding, the asymmetrical shapes of auditory filters, and a possible explanation for the deficit of the hearing impaired in noise.by Barry David Jacobson.Ph.D