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

By Michael M. Goodwin

Adaptive sign versions: conception, Algorithms and Audio Applications provides tools for deriving mathematical types of common indications. The advent covers the basics of analysis-synthesis platforms and sign representations. a number of the subject matters within the advent comprise excellent and near-perfect reconstruction, the excellence among parametric and nonparametric equipment, the position of compaction in sign modeling, easy and overcomplete sign expansions, and time-frequency solution concerns. those themes come up during the e-book as do a couple of different issues resembling filter 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 suggestions 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 lifelike synthesis, the residual needs to be individually modeled after coherent elements (such as sinusoids) are got rid of. The residual modeling technique is predicated on psychoacoustically inspired nonuniform clear out banks. bankruptcy 5 offers with pitch-synchronous models of either the wavelet and the Fourier remodel; those permit for compact versions of pseudo-periodic signs. bankruptcy Six discusses fresh algorithms for deriving sign representations in response to time-frequency atoms; essentially, the matching pursuit set of rules is reviewed and prolonged.
The sign types mentioned within the booklet are compact, adaptive, parametric, time-frequency representations which are worthwhile for research, coding, amendment, and synthesis of usual indications reminiscent of audio. The versions 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 an exceptional reference for researchers of sign processing and will be used as a textual content for complicated classes at the topic.

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Extra info for Adaptive Signal Models: Theory, Algorithms, and Audio Applications

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U j:l Q) 5- Q) Time Time-varying tiling Wavelet transform >. >. 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.

Time Tiles depicting the time-frequency localization of various expansion functions. about the signal. With this in mind, one approach to generating a set of expansion functions for signal modeling is to start with a mother tile of small area and to derive a corresponding family of tiles, each having the same area, by scaling the time and frequency widths by inverse factors and allowing for shifts in time. 33) where g(t) is the mother function. The continuous-time wavelet transform is based on families of this nature; restricting the scales and time shifts to powers of two results in the standard discrete-time wavelet transform.

3 for Ie {1, 2,3, 4}. In the simulation. N 128. K 128. and L 64; w[n] and v[n] are square-root Hanning windows. = = = = as a result the STFT does not identify this as a single evolving sinusoid but instead as a conglomeration of short-lived components, i. e. 4. Whereas this may seem useful in that it carries out a granulation of the chirp signal, inspection of the signal components shows that the subband grains are not well-localized in time; note that the transients in the original signal are manifested in all of the subband signals as pre-echoes.

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