Errors in "The Hartley Transform" by Bracewell (1986)

In the program "FHTBAS", there is one too many butterflies in the inner loop
which gives incorrect results for the last butterfly.
To correct this:

1. Change line 6130 to:
                          6130 FOR J = S0 TO N4-1 STEP S0

2. Add lines:
                          6221 I = I + 1 : D = I + S
                          6252 F(L + 1,K) = F(L,K) + F(L,E)
                          6254 F(L + 1,E) = F(L,K) - F(L,E)


In the program "FHTSUB", the same problem occurs with the inner loop so to
correct this:

1. Change line 9615 to:
                          9615 FOR J = V9(3) TO N9-1 STEP V9(3)        

2. Renumber line 9630 to 9627 and line 9631 to 9628 to allow for the addition
   of extra lines.

3. Add lines:
                          9626 I = I + 1 : D9 = I + S9 
                          9629 V9(8) = F(K9) + F(E9) : V9(9) = F(K9) - F(E9) 
                          9630 F(K9) = V9(8) : F(E0) = V9(9)

4. The calculation of Y9 is missing from the inner loop so add line:
                          9619 Y9 = X9 * T9(J) + V9(9)

I have not checked the other programs for errors although the program,
"FHTBAS.FOR" which is the Fortran version of "FHTBAS" appears at first glance
to have the same inner loop problem.

Alan Peake
June 1995

Alan.Peake@defence.dsto.gov.au OR peake@dstos3.dsto.gov.au