why definition of sine transform is not consistent with FFT?
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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~