In case of DFT where we have following $$ Y_{k}=\frac{1}{N}\sum_{n=0}^{N-1}y_ne^{-j{\frac{2\pi nk}{N}}} $$
- What happens in case when we change summation, e.g., increase or decrease number of $n$ that we are summation over?
- How does the rest of equation change? For example if we decide to sum over $NM$ (if $M<1$ we have windowing and if $M>1$ we have zero padding so I do not assume adding any new info data just scaling the duration of the signal) samples would we rewrite the latter equation like this \begin{equation} Y_{k}=\sum_{n=0}^{MN-1}y_ne^{-j{\frac{2\pi nk}{MN}}}\tag{1} \end{equation} or this \begin{equation} Y_{k}=\sum_{n=0}^{MN-1}y_ne^{-j{\frac{2\pi nk}{N}}}\quad \tag{2} \end{equation}
- And what is the explanation behind. Also what is the appropriate scaling when summation limits change?