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

By Michael M. Goodwin

Adaptive sign versions: thought, Algorithms and Audio Applications offers equipment for deriving mathematical versions of average signs. The advent covers the basics of analysis-synthesis structures and sign representations. a few of the issues within the creation comprise ideal and near-perfect reconstruction, the excellence among parametric and nonparametric equipment, the function of compaction in sign modeling, uncomplicated and overcomplete sign expansions, and time-frequency answer matters. those themes come up during the publication as do a few different subject matters comparable to clear out banks and multiresolution.
the second one bankruptcy offers a close 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 greater types. In bankruptcy 4, the analysis-synthesis residual is taken into account; for sensible synthesis, the residual has to be individually modeled after coherent elements (such as sinusoids) are got rid of. The residual modeling method relies on psychoacoustically prompted nonuniform filter out banks. bankruptcy 5 offers with pitch-synchronous models of either the wavelet and the Fourier remodel; those permit for compact types of pseudo-periodic indications. bankruptcy Six discusses contemporary algorithms for deriving sign representations in accordance with time-frequency atoms; basically, the matching pursuit set of rules is reviewed and prolonged.
The sign versions mentioned within the ebook are compact, adaptive, parametric, time-frequency representations which are worthwhile for research, coding, amendment, and synthesis of common signs akin to audio. The versions are all interpreted as equipment for decomposing a sign by way of basic time-frequency atoms; those interpretations, in addition to the adaptive and parametric natures of the versions, serve to hyperlink a few of the equipment handled within the textual content.
Adaptive sign types: conception, Algorithms and Audio Applications serves as an outstanding reference for researchers of sign processing and will be used as a textual content for complex classes at the topic.

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For such signals, unlike 44 ADAPTIVE SIGNAL MODELS in the single chirp case, all of the STFT filter bank subbands will generally have significant energy throughout the duration of the signal, so inspection of the subbands will not necessarily indicate that the various partials are moving across the bands. When all of the subbands have significant energy, it may seem reasonable to interpret the subbands as the partials of the sinusoidal model as has been discussed; this perspective, however, is in contention with the physical foundation of the natural signal.

1 Formulation of the STFT In this section, the STFT is defined and interpreted; it is shown that slightly revising the traditional definition leads to an alternative filter bank interpretation of the STFT that is appropriate for signal modeling. Perfect reconstruction constraints for such STFT filter banks are derived. In the literature, z-transform and matrix representations have been shown to be useful in analyzing the properties of such filter banks [232, 237, 238]. Here, for the sake of brevity, these methods are not explored; the STFT filter banks are treated using time-domain considerations.

For example, for a signal that consists of one linear chirp (sinusoid with linearly increasing frequency), the chirp is clearly identifiable in the distribution; for a signal consisting of two crossing chirps, the product in the integral yields cross terms that degrade the readability of the time-frequency distribution [11, 111]. These terms can be smoothed out in various ways, but always with the countereffect of decreasing the resolution of the model [118, 169, 238]. Cross terms detract from the usefulness of a quadratic time-frequency representation.

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