Download Adaptive Signal Models: Theory, Algorithms, and Audio by Michael M. Goodwin PDF

By Michael M. Goodwin

Adaptive sign versions: conception, Algorithms and Audio Applications offers equipment for deriving mathematical types of normal signs. The advent covers the basics of analysis-synthesis platforms and sign representations. the various themes within the creation comprise ideal and near-perfect reconstruction, the excellence among parametric and nonparametric equipment, the position of compaction in sign modeling, uncomplicated and overcomplete sign expansions, and time-frequency answer concerns. those issues come up in the course of the publication as do a couple of different subject matters resembling clear out banks and multiresolution.
the second one bankruptcy provides an in depth improvement of the sinusoidal version as a parametric extension of the short-time Fourier remodel. This results in multiresolution sinusoidal modeling ideas in bankruptcy 3, the place wavelet-like ways are merged with the sinusoidal version to yield more advantageous types. In bankruptcy 4, the analysis-synthesis residual is taken into account; for sensible synthesis, the residual needs to be individually modeled after coherent parts (such as sinusoids) are got rid of. The residual modeling technique relies on psychoacoustically prompted nonuniform filter out banks. bankruptcy 5 offers with pitch-synchronous models of either the wavelet and the Fourier remodel; those let for compact versions of pseudo-periodic signs. bankruptcy Six discusses fresh algorithms for deriving sign representations in line with time-frequency atoms; basically, the matching pursuit set of rules is reviewed and prolonged.
The sign types mentioned within the ebook are compact, adaptive, parametric, time-frequency representations which are invaluable for research, coding, amendment, and synthesis of typical indications similar to audio. The types are all interpreted as tools for decomposing a sign when it comes to primary time-frequency atoms; those interpretations, in addition to the adaptive and parametric natures of the types, serve to hyperlink a few of the tools handled within the textual content.
Adaptive sign types: concept, Algorithms and Audio Applications serves as a good reference for researchers of sign processing and will be used as a textual content for complex classes at the topic.

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The q-th partial pq[n] has time-varying amplitude Aq[n] and total phase 9 q[n], which describes both its frequency evolution and phase offset. The additive components in the model are thus simply parameterized by amplitude and frequency functions or tracks. These tracks are assumed to vary on a time scale substantially longer than the sampling period, meaning that the parameter tracks can be reliably estimated at a subsampled rate. This assumption of slow variation leads to compaction in the representation.

9. Tilings of the time-frequency plane for a Fourier transform, short-time Fourier transform, wavelet transform, and wavelet packet. 3 Quadratic Time-Frequency Representations Quadratic time-frequency representations or bilinear expansions have received considerable attention in the literature [35]. Fundamentally, such approaches are based on the Wigner-Ville distribution (WVD): WVD{x}(w,r) = i: x (r + ~) x (r - ~) e-;wtdt. 34) Such representations provide improved resolution over linear expansions, but at the expense of the appearance of cross terms for signals with multiple components.

4. Interpretations of the STFT. In [5, 190] and other traditional treatments of the STFT, two interpretations are considered. First, the STFT can be viewed as a series of time-localized spectra; notationally, this corresponds to 34 ADAPTIVE SIGNAL MODELS Time-localized spectrum ! 0 :>, u ~ Q) 6- Q) ~ ... 0 0 0 0 0 0 ... __ J 0 __ >-- 0 ------ . - - - -- Filter bank --~ . 1. I nterpretations of the short-time Fou rier transform as a series of time-localized spectra (vertical) and as a bank of bandpass filters (horizontal).

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