Turning Point Quantization

Turning Point Quantization and Scalet-Wavelet Analysis (C. R. Handy)... 

One is then compelled to better understand turning point quantization within a combined moment-wavelet representation. A preliminary attempt was recently presented by Handy, Murenzi, Bouyoucef, and Brooks (HMBB, 2000). A more comprehensive analysis is reviewed here, and compared to other approaches. We outline the topics covered in the following sections, although not in the didactic order presented within the Table of Contents. 

Furthermore, since CWT is the space-scale representation equivalent to the zero scale asymptotic relations in Eq.(1.5), the same conditions should also apply within the wavelet representation. We refer to this procedure as Turning Point Quantization (TPQ). 

Bearing in mind all the above, we are proposing a multiscale Turning Point Quantization (TPQ) strategy in which the large (infinite) scale structure of the quantum problem, as embodied in the EMM moments, is efficiently coupled with the local scale demands at the turning points,... 

Turning Point Quantization and Scalet- Wavelet Analysis 209 1.2 Moment Quantization... 

The second approach implements a Turning Point Quantization (TPQ) analysis within the MRF basis representation. This serves to validate the analogous formalism to be presented within the CWT discnission in the following sections (i.e. scalet-wavelet TPQ). In addition, the combined TPQ-MRF formalism allows one to identify the individual turning point contributions to the quantization process (through an analysis that explicitly incorporates all of the (complex) turning points). 

Turning Point Quantization and Scaled Wavelet Analysis 215... 

A more explicit manifestation of the coupling between large and small scale contributions, within an MRF representation, can be achieved by combining it with a Turning Point Quantization (TPQ) philosophy. Consider the N-th order MRF configuration... 

Criteria for Implementing a Turning Point Quantization Analysis... 

Turning Point Quantization in the Scalet Representation An Approximate Theory... 

Since scalets define the most efficient representation in which to study the multiscale interactions of a system, they become useful in defining a Turning Point Quantization strategy which emphasizes the democratic contribution of all the (complex) turning points of a system, as well as efficiently couples the large and small scale properties of a system. The un-... 

Handy, C. R. and Brooks, H. A., (2000) Scalets, Wavelets, emd Turning Point Quantization , preprint Clark Atlanta University. 

---