Second Order Goertzel Algorithm Below is the program for a second order Goertzel algorithm.

C----------------------------------------------
C   GOERTZEL'S  DFT  ALGORITHM
C   Second order, input inorder
C   C. S. BURRUS,   SEPT 1983
C---------------------------------------------
    SUBROUTINE DFT(X,Y,A,B,N)
    REAL X(260), Y(260), A(260), B(260)
C
    Q = 6.283185307179586/N
    DO 20 J = 1, N
       C  = COS(Q*(J-1))
       S  = SIN(Q*(J-1))
       CC = 2*C
       A2 = 0
       B2 = 0
       A1 = X(1)
       B1 = Y(1)
       DO 30 I = 2, N
          T  = A1
          A1 = CC*A1 - A2 + X(I)
          A2 = T
          T  = B1
          B1 = CC*B1 - B2 + Y(I)
          B2 = T
30     CONTINUE
       A(J) = C*A1 - A2 - S*B1
       B(J) = C*B1 - B2 + S*A1
20  CONTINUE
C
    RETURN
    END

Second Order Goertzel Algorithm