Numeric Programs

				Procedure REALFT(var DATA:array of real; N, ISIGN:integer);
				var
				    I,I1,I2,I3,I4,N2P3:integer;
				    WR,WI,C1,C2,THETA,WPR,WPI,WIS,WRS,WRI,H1R,H1I,H2R,H2I,WTEMP:real;
				begin
				    THETA:=6.28318530717959 / 2 / N;
				    C1:=0.5;
				    If ISIGN = 1 Then
				    begin
				        C2:=-0.5;
				        FOUR1(DATA, N, 1);
				    end
				    Else
				    begin
				        C2:=0.5;
				        THETA:=-THETA;
				    end; 
				    WPR:=-2* Sqr(Sin(0.5 * THETA));
				    WPI:=Sin(THETA);
				    WR:=1 + WPR;
				    WI:=WPI;
				    N2P3:= 2 * N + 3;
				    For I:=2 To (N div 2) + 1 do
				    begin
				        I1:=2 * I - 1;
				        I2:=I1 + 1;
				        I3:=N2P3 - I2;
				        I4:=I3 + 1;
				        WRS:=WR;
				        WIS:=WI;
				        H1R:=C1 * (DATA[I1] + DATA[I3]);
				        H1I:=C1 * (DATA[I2] - DATA[I4]);
				        H2R:=-C2 * (DATA[I2] + DATA[I4]);
				        H2I:=C2 * (DATA[I1] - DATA[I3]);
				        DATA[I1]:=H1R + WRS * H2R - WIS * H2I;
				        DATA[I2]:=H1I + WRS * H2I + WIS * H2R;
				        DATA[I3]:=H1R - WRS * H2R + WIS * H2I;
				        DATA[I4]:=-H1I + WRS * H2I + WIS * H2R;
				        WTEMP:=WR;
				        WR:=WR * WPR - WI * WRI + WR;
				        WI:=WI * WPR + WTEMP * WPI + WI;
				    end;
				    If ISIGN = 1 Then
				    begin
				        H1R:=DATA[1];
				        DATA[1]:=H1R + DATA[2];
				        DATA[2]:=H1R - DATA[2];
				    end
				    Else
				    begin
				        H1R:=DATA[1];
				        DATA[1]:=C1 * (H1R + DATA[2]);
				        DATA[2]:=C1 * (H1R - DATA[2]);
				        FOUR1(DATA, N, -1);
				    end; 
				end;