Factored-matrix representation of distributed fast transforms. Master's thesis
Parallel implementations of Fast Fourier Transforms (FFTs) and other fast transforms are represented using factored, partitioned matrices. The factored matrix description of a distributed FFT is introduced using a decimation in time (DIT) FFT algorithm suitable for implementation on a distributed-signal processor. The heart of the matrix representation of distributed fast transforms is the use of permutations of an NxN identity matrix to describe the required interprocessor data transfers on the Butterfly Network. The properties of these transfer matrices and the resulting output ordering are discussed in detail. The factored matrix representation is then used to show that the Fast Hartley Transform (FHT) and the Walsh Hadamard Transform (WHT) are supported by the Butterfly Network.
- Research Organization:
- Naval Postgraduate School, Monterey, CA (USA)
- OSTI ID:
- 6226905
- Report Number(s):
- AD-A-180939/1/XAB
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990210 -- Supercomputers-- (1987-1989)
ALGORITHMS
DATA PROCESSING
DISTRIBUTED DATA PROCESSING
DISTRIBUTION
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PROCESSING
PROGRAMMING
TRANSFORMATIONS