Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this work, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cram´er-Rao lower bound

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data

Audio source separation techniques including novel time-frequency representation tools

The thesis explores the development of tools for audio representation with applications in Audio Source Separation and in the Music Information Retrieval (MIR) field. A novel constant Q transform was introduced, called IIR-CQT. The transform allows a flexible design and achieves low computational cost. Also, an independent development of the Fan Chirp Transform (FChT) with the focus on the representation of simultaneous sources is studied, which has several applications in the analysis of polyphonic music signals. Dierent applications are explored in the MIR field, some of them directly related with the low-level representation tools that were analyzed. One of these applications is the development of a visualization tool based in the FChT that proved to be useful for musicological analysis . The tool has been made available as an open source, freely available software. The proposed Transform has also been used to detect and track fundamental frequencies of harmonic sources in polyphonic music. Also, the information of the slope of the pitch was used to define a similarity measure between two harmonic components that are close in time. This measure helps to use clustering algorithms to track multiple sources in polyphonic music. Additionally, the FChT was used in the context of the Query by Humming application. One of the main limitations of such application is the construction of a search database. In this work, we propose an algorithm to automatically populate the database of an existing Query by Humming, with promising results. Finally, two audio source separation techniques are studied. The first one is the separation of harmonic signals based on the FChT. The second one is an application for which the fundamental frequency of the sources is assumed to be known (Score Informed Source Separation problem)

Spectral Analysis for Signal Detection and Classification : Reducing Variance and Extracting Features

Spectral analysis encompasses several powerful signal processing methods. The papers in this thesis present methods for finding good spectral representations, and methods both for stationary and non-stationary signals are considered. Stationary methods can be used for real-time evaluation, analysing shorter segments of an incoming signal, while non-stationary methods can be used to analyse the instantaneous frequencies of fully recorded signals. All the presented methods aim to produce spectral representations that have high resolution and are easy to interpret. Such representations allow for detection of individual signal components in multi-component signals, as well as separation of close signal components. This makes feature extraction in the spectral representation possible, relevant features include the frequency or instantaneous frequency of components, the number of components in the signal, and the time duration of the components. Two methods that extract some of these features automatically for two types of signals are presented in this thesis. One adapted to signals with two longer duration frequency modulated components that detects the instantaneous frequencies and cross-terms in the Wigner-Ville distribution, the other for signals with an unknown number of short duration oscillations that detects the instantaneous frequencies in a reassigned spectrogram. This thesis also presents two multitaper methods that reduce the influence of noise on the spectral representations. One is designed for stationary signals and the other for non-stationary signals with multiple short duration oscillations. Applications for the methods presented in this thesis include several within medicine, e.g. diagnosis from analysis of heart rate variability, improved ultrasound resolution, and interpretation of brain activity from the electroencephalogram

Time-varying frequency analysis of bat echolocation signals using Monte Carlo methods

Echolocation in bats is a subject that has received much attention over the last few decades. Bat echolocation calls have evolved over millions of years and can be regarded as well suited to the task of active target-detection. In analysing the time-frequency structure of bat calls, it is hoped that some insight can be gained into their capabilities and limitations. Most analysis of calls is performed using non-parametric techniques such as the short time Fourier transform. The resulting time-frequency distributions are often ambiguous, leading to further uncertainty in any subsequent analysis which depends on the time-frequency distribution. There is thus a need to develop a method which allows improved time-frequency characterisation of bat echolocation calls. The aim of this work is to develop a parametric approach for signal analysis, specifically taking into account the varied nature of bat echolocation calls in the signal model. A time-varying harmonic signal model with a polynomial chirp basis is used to track the instantaneous frequency components of the signal. The model is placed within a Bayesian context and a particle filter is used to implement the filter. Marginalisation of parameters is considered, leading to the development of a new marginalised particle filter (MPF) which is used to implement the algorithm. Efficient reversible jump moves are formulated for estimation of the unknown (and varying) number of frequency components and higher harmonics. The algorithm is applied to the analysis of synthetic signals and the performance is compared with an existing algorithm in the literature which relies on the Rao-Blackwellised particle filter (RBPF) for online state estimation and a jump Markov system for estimation of the unknown number of harmonic components. A comparison of the relative complexity of the RBPF and the MPF is presented. Additionally, it is shown that the MPF-based algorithm performs no worse than the RBPF, and in some cases, better, for the test signals considered. Comparisons are also presented from various reversible jump sampling schemes for estimation of the time-varying number of tones and harmonics. The algorithm is subsequently applied to the analysis of bat echolocation calls to establish the improvements obtained from the new algorithm. The calls considered are both amplitude and frequency modulated and are of varying durations. The calls are analysed using polynomial basis functions of different orders and the performance of these basis functions is compared. Inharmonicity, which is deviation of overtones away from integer multiples of the fundamental frequency, is examined in echolocation calls from several bat species. The results conclude with an application of the algorithm to the analysis of calls from the feeding buzz, a sequence of extremely short duration calls emitted at high pulse repetition frequency, where it is shown that reasonable time-frequency characterisation can be achieved for these calls

Static Background Removal in Vehicular Radar: Filtering in Azimuth-Elevation-Doppler Domain

A significant challenge in autonomous driving systems lies in image understanding within complex environments, particularly dense traffic scenarios. An effective solution to this challenge involves removing the background or static objects from the scene, so as to enhance the detection of moving targets as key component of improving overall system performance. In this paper, we present an efficient algorithm for background removal in automotive radar applications, specifically utilizing a frequency-modulated continuous wave (FMCW) radar. Our proposed algorithm follows a three-step approach, encompassing radar signal preprocessing, three-dimensional (3D) ego-motion estimation, and notch filter-based background removal in the azimuth-elevation-Doppler domain. To begin, we model the received signal of the FMCW multiple-input multiple-output (MIMO) radar and develop a signal processing framework for extracting four-dimensional (4D) point clouds. Subsequently, we introduce a robust 3D ego-motion estimation algorithm that accurately estimates radar ego-motion speed, accounting for Doppler ambiguity, by processing the point clouds. Additionally, our algorithm leverages the relationship between Doppler velocity, azimuth angle, elevation angle, and radar ego-motion speed to identify the spectrum belonging to background clutter. Subsequently, we employ notch filters to effectively filter out the background clutter. The performance of our algorithm is evaluated using both simulated data and extensive experiments with real-world data. The results demonstrate its effectiveness in efficiently removing background clutter and enhacing perception within complex environments. By offering a fast and computationally efficient solution, our approach effectively addresses challenges posed by non-homogeneous environments and real-time processing requirements