By Michael M. Goodwin
Adaptive sign versions: conception, Algorithms and Audio Applications offers tools for deriving mathematical types of traditional signs. The advent covers the basics of analysis-synthesis structures and sign representations. many of the themes within the creation comprise ideal and near-perfect reconstruction, the excellence among parametric and nonparametric equipment, the position of compaction in sign modeling, simple and overcomplete sign expansions, and time-frequency solution concerns. those issues come up during the ebook as do a couple of different themes akin to 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 ends up in multiresolution sinusoidal modeling suggestions in bankruptcy 3, the place wavelet-like methods are merged with the sinusoidal version to yield superior types. In bankruptcy 4, the analysis-synthesis residual is taken into account; for real looking synthesis, the residual has to be individually modeled after coherent elements (such as sinusoids) are got rid of. The residual modeling process relies on psychoacoustically prompted nonuniform clear out banks. bankruptcy 5 offers with pitch-synchronous types of either the wavelet and the Fourier remodel; those permit for compact types of pseudo-periodic signs. bankruptcy Six discusses contemporary algorithms for deriving sign representations according to time-frequency atoms; essentially, 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 worthwhile for research, coding, amendment, and synthesis of traditional signs comparable 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 equipment handled within the textual content.
Adaptive sign types: thought, Algorithms and Audio Applications serves as a superb reference for researchers of sign processing and should be used as a textual content for complex classes at the topic.
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Additional info for Adaptive Signal Models: Theory, Algorithms, and Audio Applications
The matching pursuit is inherently nonlinear in the way it selects the expansion functions from the overcomplete dictionary; it overcomes the inadequacies of linear methods such as the SVD while providing for successive refinement and compact sparse approximations. It has been argued that overcompleteness, when coupled with a nonlinear analysis, yields a signal-adaptive representation, so these notions are tightly coupled [42, 94]. Atomic models. Finally, all of the models in this book can be interpreted in terms of localized time-frequency atoms or grains.
This means that some modifications of the expansion coefficients, namely those that correspond to adding vectors in the null space of the dictionary matrix D, will have no effect on the reconstruction. This may seem to be at odds with the previous assertion that compact models are useful for modification, but this is not necessarily the case. If fundamental signal structures are isolated as in compact models, the corresponding coefficients and functions can be modified jointly to avoid such difficulties.
Finally, frequency localization is of interest because of the relationship of frequency to pitch in audio signals, and because of the importance of frequency in understanding the behavior of linear systems. 29) are of special interest when the expansion functions 9i[n] are localized in timefrequency, since such expansions indicate the local time-frequency characteristics of a signal. Such cases, first elaborated by Gabor from both theoretical and psychoacoustic standpoints [74, 75], are referred to as time-frequency atomic decompositions; the localized functions 9i[n] are time-frequency, fundamental particles which comprise natural signals.