Time-Frequency Synthesis of Linear Signal Spaces
So far, we have considered the TF analysis of linear signal spaces by means of the WD of a linear signal space. In this chapter, we present a framework and a method for the optimum TF synthesis of linear signal spaces using the WD. The synthesis problem is formulated as finding the space with optimum localization in a given region of the TF plane. In other words, all signals of the optimum space are effectively located inside the given TF region, in such a manner that the TF region is “filled energetically” by the space while only a minimum amount of space energy leaks to the outside of the TF region. Mathematically, this synthesis problem can be formulated as a minimization of the space’s TF localization error as introduced in the previous chapter.
KeywordsOrthonormal Basis Optimum Dimension Synthesis Problem Signal Space Optimum Space
Unable to display preview. Download preview PDF.