Time-Frequency Filters and Time-Frequency Expansions
The separation of signal components occupying effectively disjoint regions of the TF plane is a fundamental problem of TF signal processing that is encountered in many applications. A related problem is the parsimonious representation (expansion) of signals located in a given TF region. In this chapter, we propose solutions to both problems. These solutions are based on the optimum space synthesis (eigenspaces) described in the previous chapter. A “TF projection filter” for signal separation is obtained as the orthogonal projection operator on the eigenspace of the given TF pass region, and a “TF expansion” is based on any orthonormal basis of the eigenspace of the given TF support region.
KeywordsFilter Bank Pass Region Residual Space Orthogonal Projection Operator Weyl Symbol
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