Large symmetric. pi. transformations for Hadamard transforms
Many multiplexing instruments utilize the fast Hadamard transform (FHT) to demultiplex the signal. In the past, the HFT includes the ..pi../sub 1/ and ..pi../sub 2/ transformations to reorder vectors before and after a Sylvester-type Hadamard transform. Although the computational effort involved in the ..pi../sub 1/ and the Sylvester-type Hadamard transform scales as n log/sub 2/n, calculating the ..pi../sub 2/ transformation (which only has to be done once) scales as n/sup 2/. Recently Gunson (1980) has suggested a method by which the ..pi.. transformations are symmetric, that is ..pi../sub 2/ = ..pi../sub 1/. We have calculated a complete set of symmetric ..pi.. transformations for FHT of sizes 2/sup 3/ to 2/sup 30/. Special emphasis has been placed on the phase of the ..pi.. transformation so as to have the correct phase in the demultiplexed signal.
- Research Organization:
- University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 97545
- OSTI ID:
- 6029620
- Journal Information:
- Appl. Opt.; (United States), Vol. 22:6
- Country of Publication:
- United States
- Language:
- English
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