{FOURIER.TLD Prozeduren und Funktionen :
procedure fourier_analysis(y : RealArrayType_TL;
  var  a,b : RealArrayType_TL;
  n        : integer);
function fourier_synthesis(x : real;
  a,b     : RealArrayType_TL;
  n       : integer;
  min,max : real) : real;
}

procedure fourier_analysis(y : RealArrayType_TL;
  var a,b : RealArrayType_TL;
  n       : integer);
var dummy,u0,u1,u2,coeff,c0,s0,c,s:real;
  i,k:integer;
begin
  n:=pred(n);
  coeff:=2.0/n;
  c0:=cos(coeff*pi);
  s0:=sin(coeff*pi);
  c:=1.0;s:=0.0;
  for k:=0 to pred(n) div 2 do
  begin
    u1:=0.0;u2:=0.0;
    for i:=pred(n) downto 1 do
    begin
      u0:=y[succ(i)]+2.0*c*u1-u2;
      u2:=u1;
      u1:=u0;
    end;
    a[succ(k)]:=coeff*(y[1]+c*u1-u2);
    b[succ(k)]:=coeff*s*u1;
    dummy:=c*c0-s*s0;
    s:=s*c0+c*s0;
    c:=dummy;
  end;
  a[1]:=a[1]/2.0;
end;

function fourier_synthesis(x : real;
  a,b     : RealArrayType_TL;
  n       : integer;
  min,max : real) : real;
var i:integer;
  sum:real;
begin
  if (min<0.0) or (max>2.0*pi) then x:=(x-min)/(max-min)*2.0*pi;
  sum:=0;
  for i:=2 to n div 2 do sum:=sum+a[i]*cos(pred(i)*x)+b[i]*sin(pred(i)*x);
  fourier_synthesis:=sum+a[1]/2.0;
end;