I am performing FFT on a real odd function and the resultant transform has zero amplitude in the last bin. Essentially if Y= rfft(X), then Y[-1] is always zero. I stumbled on this answer which says
An anti-symmetric waveform has to be zero at the center of an even length window.
Now, this might be very easy to prove but I cannot think of why this is true. If I use the formula then to the first term should be zero, not $N/2$ th. It's clear to me why it should be real but why should the amplitude be zero for real-valued, odd function. Any help will be appreciated.