C     SUBROUTINE SINQB(N,X,WSAVE)                                               
C                                                                               
C     SUBROUTINE SINQB COMPUTES THE FAST FOURIER TRANSFORM OF QUARTER           
C     WAVE DATA. THAT IS , SINQB COMPUTES A SEQUENCE FROM ITS                   
C     REPRESENTATION IN TERMS OF A SINE SERIES WITH ODD WAVE NUMBERS.           
C     THE TRANSFORM IS DEFINED BELOW AT OUTPUT PARAMETER X.                     
C                                                                               
C     SINQF IS THE UNNORMALIZED INVERSE OF SINQB SINCE A CALL OF SINQB          
C     FOLLOWED BY A CALL OF SINQF WILL MULTIPLY THE INPUT SEQUENCE X            
C     BY 4*N.                                                                   
C                                                                               
C     THE ARRAY WSAVE WHICH IS USED BY SUBROUTINE SINQB MUST BE                 
C     INITIALIZED BY CALLING SUBROUTINE SINQI(N,WSAVE).                         
C                                                                               
C                                                                               
C     INPUT PARAMETERS                                                          
C                                                                               
C     N       THE LENGTH OF THE ARRAY X TO BE TRANSFORMED.  THE METHOD          
C             IS MOST EFFICIENT WHEN N IS A PRODUCT OF SMALL PRIMES.            
C                                                                               
C     X       AN ARRAY WHICH CONTAINS THE SEQUENCE TO BE TRANSFORMED            
C                                                                               
C     WSAVE   A WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 3*N+15.           
C             IN THE PROGRAM THAT CALLS SINQB. THE WSAVE ARRAY MUST BE          
C             INITIALIZED BY CALLING SUBROUTINE SINQI(N,WSAVE) AND A            
C             DIFFERENT WSAVE ARRAY MUST BE USED FOR EACH DIFFERENT             
C             VALUE OF N. THIS INITIALIZATION DOES NOT HAVE TO BE               
C             REPEATED SO LONG AS N REMAINS UNCHANGED THUS SUBSEQUENT           
C             TRANSFORMS CAN BE OBTAINED FASTER THAN THE FIRST.                 
C                                                                               
C     OUTPUT PARAMETERS                                                         
C                                                                               
C     X       FOR I=1,...,N                                                     
C                                                                               
C                  X(I)= THE SUM FROM K=1 TO K=N OF                             
C                                                                               
C                    4*X(K)*SIN((2K-1)*I*PI/(2*N))                              
C                                                                               
C                  A CALL OF SINQB FOLLOWED BY A CALL OF                        
C                  SINQF WILL MULTIPLY THE SEQUENCE X BY 4*N.                   
C                  THEREFORE SINQF IS THE UNNORMALIZED INVERSE                  
C                  OF SINQB.                                                    
C                                                                               
C     WSAVE   CONTAINS INITIALIZATION CALCULATIONS WHICH MUST NOT               
C             BE DESTROYED BETWEEN CALLS OF SINQB OR SINQF.                     
C                                                                               
      SUBROUTINE SINQB (N,X,WSAVE)                                              
      DIMENSION       X(*)       ,WSAVE(*)                                      
C                                                                               
      IF (N .GT. 1) GO TO 101                                                   
      X(1) = 4.*X(1)                                                            
      RETURN                                                                    
  101 NS2 = N/2                                                                 
      DO 102 K=2,N,2                                                            
         X(K) = -X(K)                                                           
  102 CONTINUE                                                                  
      CALL COSQB (N,X,WSAVE)                                                    
      DO 103 K=1,NS2                                                            
         KC = N-K                                                               
         XHOLD = X(K)                                                           
         X(K) = X(KC+1)                                                         
         X(KC+1) = XHOLD                                                        
  103 CONTINUE                                                                  
      RETURN                                                                    
      END