Multirate Time-Frequency Distributions
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Multirate systems, which find application in the design and analysis of filter banks, are demonstrated to also be useful as a computational paradigm. It is shown that any problem which can be expressed a set of vector-vector, matrix-vector or matrix-matrix operations can be recast using multirate. This means all of numerical linear algebra can be recast using multirate as the underlying computational paradigm. As a non-trivial example, the multirate computational paradigm is applied to the problem of Generalized Discrete Time- Frequency Distributions GDTFD to create a new family of fast algorithms. The first of this new class of distributions is called the Decimated GDTFD D-GDTFD . These distributions trade bandwidth for speed. For a decimation factor of m, there is an in fold increase in throughput. The D-GDTFD requires significantly less storage than the GDTFD, only 1m2 of the storage of the GDTFD. By combining several D-GDTFDs, it is possible to reconstruct a GDTFD. This reconstruction of DGDTFDs is the Multirate Time-Frequency Distribution MRTFD. If the individual D-GDTFDs can also be implemented in parallel, improvement in throughput on the order of m 2 or more results. Multirate, Time-frequency distribution, Decimated time-frequency distribution, Fast algorithms.
- Numerical Mathematics