SINQF(3)

SYNOPSIS
SUBROUTINE SINQF (N, X, WSAVE)

NAME
sinqf - Compute the forward sine transform with odd wave numbers.

LIBRARY
SLATEC (FFTPACK)

CATEGORY
J1A3

TYPE
SINGLE PRECISION (SINQF-S)

KEYWORDS
FFTPACK, FOURIER TRANSFORM

AUTHOR
Swarztrauber, P. N., (NCAR)

DESCRIPTION
Subroutine SINQF computes the fast Fourier transform of quarter wave data. That is, SINQF computes the coefficients in a sine series representation with only odd wave numbers. The transform is defined below at output parameter X. SINQB is the unnormalized inverse of SINQF since a call of SINQF followed by a call of SINQB will multiply the input sequence X by 4*N. The array WSAVE which is used by subroutine SINQF must be initialized by calling subroutine SINQI(N,WSAVE). Input Parameters N the length of the array X to be transformed. The method is most efficient when N is a product of small primes. X an array which contains the sequence to be transformed WSAVE a work array which must be dimensioned at least 3*N+15 in the program that calls SINQF. The WSAVE array must be initialized by calling subroutine SINQI(N,WSAVE), and a different WSAVE array must be used for each different value of N. This initialization does not have to be repeated so long as N remains unchanged. Thus subsequent transforms can be obtained faster than the first. Output Parameters X For I=1,...,N X(I) = (-1)**(I-1)*X(N) + the sum from K=1 to K=N-1 of 2*X(K)*SIN((2*I-1)*K*PI/(2*N)) A call of SINQF followed by a call of SINQB will multiply the sequence X by 4*N. Therefore SINQB is the unnormalized inverse of SINQF. WSAVE contains initialization calculations which must not be destroyed between calls of SINQF or SINQB.

REFERENCES
P. N. Swarztrauber, Vectorizing the FFTs, in Parallel Computations (G. Rodrigue, ed.), Academic Press, 1982, pp. 51-83.

ROUTINES CALLED
COSQF

REVISION HISTORY (YYMMDD)
790601 DATE WRITTEN
830401 Modified to use SLATEC library source file format.
860115 Modified by Ron Boisvert to adhere to Fortran 77 by changing dummy array size declarations (1) to (*)
861211 REVISION DATE from Version 3.2
881128 Modified by Dick Valent to meet prologue standards.
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)