From paper:
Bradford R., Dobson R., ffitch J. - Sliding is Smoother than jumping
In chapter 6 - Signal Reconstruction, the inverse of the sliding DFT can be achieved by this formula:
$$f_0=\frac{1}{N}\sum_{k=0}^{N-1}F_0(k)e^{-2\pi i k (0/N)} = \frac{1}{N}\sum_{k-=0}^{N-1}F_0(k)$$
In other words, the average of all the frequency bins is equal to the first sample of the window.
But I wonder, if the input signal is a single sine wave, then the DFT of the signal will be the same throughout the whole signal. And then using the above formula, the resynthesized samples are all going to be the same number, when in reality it has to vary from -1 to 1.
Am I understanding this wrong?
I made a picture describing my question: