why definition of sine transform is not consistent with FFT?

See the picture.

Let's suppose: G(f) = DST(g(t)) and G(f) = FFT(g(t))

There are inconsistency in 2 things:

1. sine transform uses sin(pi*f*t) while fft uses exp(i*2*pi*f*t) --- *2 is the difference

The sine transform I learn from books uses sin(2*pi*f*t)

The definition of sine transform in Matlab actually gives a result of G(f/2)

2. fft starts with (j-1) and (k-1) in the exponential while sine transform starts with n and k ---- missed 0 frequency term

Anybody know why it's defined like this? Any ideas are appreciated. Thanks~

[Yuji Zhang]

anybody? any thoughts are appreciated. Thanks~~

[Amith Kamath]

If you look at the source for dst,

edit dst

you can see that it uses the real part of the FFT computation. Can you share some examples of why you think the documentation is inaccurate? This may be useful for someone to verify that it is indeed incorrect.