Damped and delayed sinuosidal model for transient modeling

International audienceIn this work, we present the Damped and De- layed Sinusoidal (DDS) model, a generalization of the sinu- soidal model. This model takes into account an angular fre- quency, a damping factor, a phase, an amplitude and a time- delay parameter for each component. Two algorithms are introduced for the DDS parameter estimation using a sub- band processing approach. Finally, we derive the Cramer- Rao Bound (CRB) expression for the DDS model and a simulation-based performance analysis in the context of a noisy fast time-varying synthetic signal and in the audio transient signal modeling context

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

Transient and steady-state component separation for audio signals

In this work the problem of transient and steady-state component separation of an audio signal was addressed. In particular, a recently proposed method for separation of transient and steady-state components based on the median filter was investigated. For a better understanding of the processes involved, a modification of the filtering stage of the algorithm was proposed. This modification was evaluated subjectively by listening tests and objectively by an application-based comparison. Also some extensions to the model were presented in conjunction with different possible applications for the transient and steady-state decomposition in the area of audio editing and processing

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

Toward an interpretive framework of two-dimensional speech-signal processing

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 177-179).Traditional representations of speech are derived from short-time segments of the signal and result in time-frequency distributions of energy such as the short-time Fourier transform and spectrogram. Speech-signal models of such representations have had utility in a variety of applications such as speech analysis, recognition, and synthesis. Nonetheless, they do not capture spectral, temporal, and joint spectrotemporal energy fluctuations (or "modulations") present in local time-frequency regions of the time-frequency distribution. Inspired by principles from image processing and evidence from auditory neurophysiological models, a variety of twodimensional (2-D) processing techniques have been explored in the literature as alternative representations of speech; however, speech-based models are lacking in this framework. This thesis develops speech-signal models for a particular 2-D processing approach in which 2-D Fourier transforms are computed on local time-frequency regions of the canonical narrowband or wideband spectrogram; we refer to the resulting transformed space as the Grating Compression Transform (GCT). We argue for a 2-D sinusoidal-series amplitude modulation model of speech content in the spectrogram domain that relates to speech production characteristics such as pitch/noise of the source, pitch dynamics, formant structure and dynamics, and offset/onset content. Narrowband- and wideband-based models are shown to exhibit important distinctions in interpretation and oftentimes "dual" behavior. In the transformed GCT space, the modeling results in a novel taxonomy of signal behavior based on the distribution of formant and onset/offset content in the transformed space via source characteristics. Our formulation provides a speech-specific interpretation of the concept of "modulation" in 2-D processing in contrast to existing approaches that have done so either phenomenologically through qualitative analyses and/or implicitly through data-driven machine learning approaches. One implication of the proposed taxonomy is its potential for interpreting transformations of other time-frequency distributions such as the auditory spectrogram which is generally viewed as being "narrowband"/"wideband" in its low/high-frequency regions. The proposed signal model is evaluated in several ways. First, we perform analysis of synthetic speech signals to characterize its properties and limitations. Next, we develop an algorithm for analysis/synthesis of spectrograms using the model and demonstrate its ability to accurately represent real speech content. As an example application, we further apply the models in cochannel speaker separation, exploiting the GCT's ability to distribute speaker-specific content and often recover overlapping information through demodulation and interpolation in the 2-D GCT space. Specifically, in multi-pitch estimation, we demonstrate the GCT's ability to accurately estimate separate and crossing pitch tracks under certain conditions. Finally, we demonstrate the model's ability to separate mixtures of speech signals using both prior and estimated pitch information. Generalization to other speech-signal processing applications is proposed.by Tianyu Tom Wang.Ph.D

Spectral Modelling for Transformation and Separation of Audio Signals

The Short-Time Fourier Transform is still one of the most prominent time-frequency analysis techniques in many fields, due to its intuitive nature and computationally-optimised basis functions. Nevertheless, it is far from being the ultimate solution as it is plagued with a variety of assumptions and user-specific design choices, which result in a number of compromises. Numerous attempts have been made to circumvent its inevitable internal deficiencies, which include fixed time-frequency resolutions, static sample points, and highly biased outputs. However, its most important assumption, stationarity, is yet to be dealt with effectively. A new concept is proposed, which attempts to improve the credibility of the STFT results by allowing a certain degree of deviation from stationarity to be incorporated into the analysis. This novel approach utilises an ensemble of estimates instead of a single estimation in order to investigate the short-time phase behaviour of every frequency bin. The outcome is the definition of a quality measure, phase stability, that discriminates the "structured" from the "artefact" frequency components. This quality measure is then used in the framework of source separation as a single application example where it is possible to investigate its potential on the performance of the algorithm. Specifically, it was used in the spectral peak picking step of a numerical model-based source separation algorithm. It was found that the phase stability quality measure acts as an effective data reduction tool, which qualifies it as a more appropriate thresholding technique than the conventional methods. Based on this example, it is anticipated that this new method has great potential. Its ability to discriminate between "structured" and "noise" or edge effect/"artefacts" qualifies it as a promising new tool that can be added in the arsenal of the STFT modifications and used in the development of a hybrid super-STFT

Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription

This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci

Towards Real-Time Non-Stationary Sinusoidal Modelling of Kick and Bass Sounds for Audio Analysis and Modification

Sinusoidal Modelling is a powerful and flexible parametric method for analysing and processing audio signals. These signals have an underlying structure that modern spectral models aim to exploit by separating the signal into sinusoidal, transient, and noise components. Each of these can then be modelled in a manner most appropriate to that component's inherent structure. The accuracy of the estimated parameters is directly related to the quality of the model's representation of the signal, and the assumptions made about its underlying structure. For sinusoidal models, these assumptions generally affect the non-stationary estimates related to amplitude and frequency modulations, and the type of amplitude change curve. This is especially true when using a single analysis frame in a non-overlapping framework, where biased estimates can result in discontinuities at frame boundaries. It is therefore desirable for such a model to distinguish between the shape of different amplitude changes and adapt the estimation of this accordingly. Intra-frame amplitude change can be interpreted as a change in the windowing function applied to a stationary sinusoid, which can be estimated from the derivative of the phase with respect to frequency at magnitude peaks in the DFT spectrum. A method for measuring monotonic linear amplitude change from single-frame estimates using the first-order derivative of the phase with respect to frequency (approximated by the first-order difference) is presented, along with a method of distinguishing between linear and exponential amplitude change. An adaption of the popular matching pursuit algorithm for refining model parameters in a segmented framework has been investigated using a dictionary comprised of sinusoids with parameters varying slightly from model estimates, based on Modelled Pursuit (MoP). Modelling of the residual signal using a segmented undecimated Wavelet Transform (segUWT) is presented. A generalisation for both the forward and inverse transforms, for delay compensations and overlap extensions for different lengths of Wavelets and the number of decomposition levels in an Overlap Save (OLS) implementation for dealing with convolution block-based artefacts is presented. This shift invariant implementation of the DWT is a popular tool for de-noising and shows promising results for the separation of transients from noise