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Author
Title Non-stationary sinusoidal analysis
URL
Publication Date
Date Accessioned
Discipline/Department Departament de Tecnologies de la Informació i les Comunicacions
University/Publisher Universitat Pompeu Fabra
Abstract Many types of everyday signals fall into the non-stationary sinusoids category. A large family of such signals represent audio, including acoustic/electronic, pitched/transient instrument sounds, human speech/singing voice, and a mixture of all: music. Analysis of such signals has been in the focus of the research community for decades. The main reason for such intense focus is the wide applicability of the research achievements to medical, financial and optical applications, as well as radar/sonar signal processing and system analysis. Accurate estimation of sinusoidal parameters is one of the most common digital signal processing tasks and thus represents an indispensable building block of a wide variety of applications. Classic time-frequency transformations are appropriate only for signals with slowly varying amplitude and frequency content - an assumption often violated in practice. In such cases, reduced readability and the presence of artefacts represent a significant problem. Time and frequency resolu
Subjects/Keywords Sinusoidal analysis; Non-stationary sinusoid; Amplitude modulation; Frequency modulation; Polynomial phase; Generalised sinusoid; Complex polynomial amplitude modulated complex sinusoid with exponential damping; cPACE, cPACED, PACE; Overapping sinusoids; Non-linear analysis; Kernel based analysis; Linear systems of equations; Non-linear systems of equations; Multivariate polynomial systems; Energy reallocation; Reassignment; Generalised reassignment; Distribution derivative; Derivative method; Sinusoidal parameter estimation; Sound analysis; High-resolution analysis; Transient analysis; Time-frequency distributions; Chebyshev polynomial; Adaptive signal analysis; Gamma function; 62
Contributors [email protected] (authoremail); true (authoremailshow); Serra, Xavier (director); Bonada, Jordi, 1973- (director); true (authorsendemail)
Language en
Rights L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess [Always confirm rights and permissions with the source record.]
Country of Publication es
Record ID handle:10803/123809
Repository barcelona
Date Indexed 2019-12-30
Issued Date 2013-09-10 00:00:00

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…T where the window function is assumed to be non-zero only for t ∈ − T 2, 2 acting as the limits of integration in equation 1.3. It is now trivial to generalise the complex exponential to an arbitrary kernel Ψ(t): s(t), w(t…

…x29;Ψ(t) . (1.7) Adopting the use of an arbitrary kernel allows for a very important flexibility when the signal under study does not correlate strongly with a stationary complex exponential, inevitably leading to numerical…

…some accuracy. Generally, iterative improvement methods will be avoided when possible, due to difficulties of defining the convergence region when dealing with real world signals. Specifically, a number of state-of-the-art kernel based methods are…

…described, evaluated and improved. In addition, a new family of estimators is proposed and evaluated. This dissertation will cover two main sinusoidal models: a complex polynomial amplitude modulated complex sinusoid with exponential damping (cPACED…

…71 5 Reassignment with adaptive Fourier poly-phase 5.1 GRM using a generic kernel . . . . . . . . . . . . 5.2 Polynomial-phase Fourier kernel . . . . . . . . . 5.3 Tests and Results . . . . . . . . . . . . . . . . . . 5.4 Conclusion…

…6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . kernel . . . . . . . . . . . . . . . . . . . . model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 77 78 80 81 . . . . . 85 86 88 91 91 94 7 Non-stationary…

…8.1 8.2 9.1 9.2 . 117 . 118 . 120 . 122 Amplitude polynomial and exponential damping estimates separately (above) and cumulative (below). . . . . . . . . . . . . . . 125 SRR: Mean and variance…

…utilise a test function, sometimes called a kernel or an atom, the difference between the estimation and representation can be substantially blurred. A small set of kernels is commonly required for a single estimation. Typically the kernels centred around…

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