-- Generic_Complex_Fast_Fourier_Transform

with ARRAY_EXCEPTIONS;

generic -- package YOUR_NAME is new GENERIC_COMPLEX_FAST_FOURIER_TRANSFORM
        --     ( REAL, COMPLEX, COMPLEX_VECTOR, COMPLEX_MATRIX);
        --        do the instantiation where the instantiation of
        --        GENERIC_COMPLEX_TYPES is visible

  type REAL is digits <> ;
  type COMPLEX is private;
  type COMPLEX_VECTOR is array(INTEGER range <>) of COMPLEX;
  type COMPLEX_MATRIX is array(INTEGER range <>,INTEGER range <>) of COMPLEX;
  with function COMPOSE_FROM_CARTESIAN(L,R:REAL) return COMPLEX is <>;
  with function RE(L:COMPLEX) return REAL is <>;
  with function IM(L:COMPLEX) return REAL is <>;
  with function "+"(L,R:COMPLEX) return COMPLEX is <>;
  with function "-"(L,R:COMPLEX) return COMPLEX is <>;
  with function "*"(L,R:COMPLEX) return COMPLEX is <>;
  with function "/"(L,R:COMPLEX) return COMPLEX is <>;
  with function "*"(L:COMPLEX;R:REAL) return COMPLEX is <>;
  with function "/"(L:COMPLEX;R:REAL) return COMPLEX is <>;

package GENERIC_COMPLEX_FAST_FOURIER_TRANSFORM is
  
  procedure FFT ( A : in out COMPLEX_VECTOR ) ;
  function  FFT ( A : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;

  --      PURPOSE : COMPUTE DISCRETE FAST FOURIER TRANSFORM OF
  --                THE POINTS IN THE COMPLEX VECTOR
  --
  --      INPUT : THE COMPLEX VECTOR A ( e.g. TIME DOMAIN )
  --
  --      OUTPUT : THE TRANSFORM OF VECTOR A ( e.g. FREQUENCY DOMAIN )
  --               IS RETURNED IN PLACE FOR THE PROCEDURE,
  --               IS RETURNED AS THE VALUE OF THE FUNCTION
  --               SCALED BY DIVIDING BY NUMBER OF POINTS
  --
  --      METHOD : N LOG N FFT ALGORITHM

  procedure INVERSE_FFT ( A : in out COMPLEX_VECTOR ) ;
  function  INVERSE_FFT ( A : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;

  --      PURPOSE : COMPUTE INVERSE DISCRETE FAST FOURIER TRANSFORM OF
  --                THE POINTS IN THE COMPLEX VECTOR
  --
  --      INPUT : THE COMPLEX VECTOR A ( e.g. FREQUENCY DOMAIN )
  --
  --      OUTPUT : THE INVERSE TRANSFORM OF VECTOR A ( e.g. TIME DOMAIN )
  --               IS RETURNED IN PLACE FOR THE PROCEDURE,
  --               IS RETURNED AS THE VALUE OF THE FUNCTION
  --               NO SCALING
  --
  --      METHOD : N LOG N FFT ALGORITHM

  procedure FEJER ( A : in out COMPLEX_VECTOR ) ;
  function  FEJER ( A : COMPLEX_VECTOR ) return COMPLEX_VECTOR ;

  --      PURPOSE : COMPUTE FEJER MODIFIED FOURIER TRANSFORM OF
  --                THE POINTS IN THE COMPLEX VECTOR
  --
  --      INPUT : THE COMPLEX VECTOR A ( e.g. TIME DOMAIN )
  --
  --      OUTPUT : THE FEJER TRANSFORM OF VECTOR A ( e.g. FREQUENCY DOMAIN )
  --               IS RETURNED IN PLACE FOR THE PROCEDURE,
  --               IS RETURNED AS THE VALUE OF THE FUNCTION
  --
  --      METHOD : N LOG N FFT ALGORITHM
  --               APPLY WEIGHTING OF (N-I)/N TO I TH FREQUENCY
  --               WHERE N IS THE LENGHT OF THE VECTOR

end GENERIC_COMPLEX_FAST_FOURIER_TRANSFORM ;