Let x=[1, ⋯ ,1, 0, ⋯ ,0] be a window vector of length N, which consists of B consecutive 1s and the remaining N-B consecutive 0s.
I took the N-point DFT on x and got X=[X_0, X_1, ⋯, X_(N-1)] which is the result of the DFT.
I tried to show that the maximum absolute value of X_k, where k=1, ⋯, N-1, is always when k=1, for any B=1, ⋯,N.
(when k=0, it is trivial that X_0=B)
My approach was as follows:
Click and see the "The maximum absolute value of DFT of window vector" post: http://taekyo11.tistory.com/
Could anybody please help me figure out |X_k| is at peak when k=1?
I am strongly convinced that it is true through computer simulations and my intuition with the shape of cosecant function also suggests the same result, but I could not be successful mathematically.
May some kind person help me!
Thank you very much.