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		COOLEY-TUKEY FAST FOURIER TRANSFORMS




THIS TAPE CONTAINS THE FOLLOWING FILES:

1.)	CTFFT.DOC	THIS FILE
2.)	CTFFT.F4	A 1-DIMENTIONAL FFT SUBROUTINE (FOURG)
3.)	TESTF.F4	A TEST ROUTINE FOR FOURG
4.)	TESTF.OUT	THE OUTPUT PRODUCED BY TESTF
5.)	CTFFTM.F4	A MULTI-DIMENTIONAL FFT SUBROUTINE(FOUR2)
6.)	TESTFM.F4	A TEST ROUTINE FOR FOUR2
7.)	TESTFM.OUT	THE OUTPUT FROM  TESTFM


ALL PROGRAMS ARE REASONABLY WELL DOCUMENTED.  THE
LISTINGS  SHOULD BE READ BY ANYONE DESIRING TO USE
THE PROGRAMS.

SOME POINTS OF INTEREST ARE:

1.)	TEST PROGRAM OUTPUT IS WRITTEN TO DEVICE # 6

2.)	ABOUT 58% OF THE TIME TO RUN TESTF WITH
	THE SUPPLIED DATA IS SPENT IN FOURG (NATURALLY)
	IN THE CODE FOLLOWING STATEMENT 180 (I.E.
	LINES FFG121-FFG125.

3.)	THIS SAME PROGRAM AND DATA HAS BEEN
	RUN ON A CDC-6400 (FTN V3.0 OPT=1) UNDER
	SCOPE 3.2 WITH AN

		RMS RELATIVE ERROR =   .6867E-07

	WHICH CORRESPONDS TO DOUBLE PRECISION ON THE 
	DECSYSTEM-10.

4.)	THE FOUR2-TESTFM PROGRAM WAS RUN ON A 32-BIT HEX
	MACHINE WITH SOMEWHAT LESS PERFORMANCE:

	ARRAY	    RMS RELATIVE ERROR
	SIZE	32-BIT     	DECSYSTEM-10
	8 X 2	.4771E-06	.4395E-08
	8 X 32	.1051E-05	.1906E-07
	8 X128	.3590E-05	.4255E-07
	8 X512	.2543E-04	.2046E-06

5.)	THESE PROGRAMS ARE NOT SUPPORTED HOWEVER PLEASE
	SEND ANY COMMENTS,SUGGESTIONS, COMPLAINTS
	ETC. TO:

		ASHLEY D. GRAYSON
		DECSYSTEM-10 SCIENTIFIC MARKETING
		DIGITAL EQUIPMENT CORPORATION
		146 MAIN STREET
		MAYNARD, MASS. 01754