[Mp4-tech] HE-AAC downsampled synthesis filterbank

[Andy Quan]

Hi folks,
I read the ISO spec 14496-3 Amd 1 on downsampled complex synthesis QMF
filter. On page 67, it is said the filterbank coefficients are defined
as (1/64)*exp(i*pi*(k+.5)*(2*n-127)/64).
However, when I turn to the ISO reference, in ct_polyphase.c, the code
defines the coefficients like:cos( PI / 64.0 * (k+0.5) * (2*l-127.5)
).
My question is why the spec uses 127 while its reference code
implementation uses 127.5. I don't understand this 0.5 trick. Can any
one explain this for me? Thanks in advance.
-- 
Regards,
Andy Quan